mod int64 7 7 | ops_mode stringclasses 1
value | question stringlengths 215 361 | preamble stringclasses 1
value | equations stringlengths 31 177 | query stringclasses 64
values | answer int64 0 6 | cot stringlengths 34 616 | operator_table listlengths 4 4 | target_depth int64 2 4 | achieved_depth int64 2 4 | num_vars int64 3 11 | num_necessary int64 2 9 | num_distractors int64 0 0 | var_layer unknown | id stringlengths 18 18 |
|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
7 | arith | Operator definitions (evaluate strictly left to right, all results mod 7): a + b = (a + b) mod 7 a - b = (a - b) mod 7 a * b = (a × b) mod 7 a / b = (a × b⁻¹) mod 7 [b≠0].
F#J := 3. G#M := 3. H#I := F#J / G#M. H#I? | Operator definitions (evaluate strictly left to right, all results mod 7): a + b = (a + b) mod 7 a - b = (a - b) mod 7 a * b = (a × b) mod 7 a / b = (a × b⁻¹) mod 7 [b≠0]. | F#J := 3. G#M := 3. H#I := F#J / G#M. | H#I | 1 | F#J = 3 -> F#J = 3
G#M = 3 -> G#M = 3
H#I = F#J / G#M
= 3 / 3
3 / 3 = (3 × 3⁻¹) mod 7 = 1
=> H#I = 1 | [
{
"glyph": "+",
"kind": "add",
"params": {},
"definition": "a + b = (a + b) mod 7"
},
{
"glyph": "-",
"kind": "sub",
"params": {},
"definition": "a - b = (a - b) mod 7"
},
{
"glyph": "*",
"kind": "mul",
"params": {},
"definition": "a * b = (a × b) mod 7"
},
... | 2 | 2 | 3 | 3 | 0 | {
"F#J": 1,
"G#M": 1,
"H#I": 2
} | mod7_arith_d2_0000 |
7 | arith | Operator definitions (evaluate strictly left to right, all results mod 7): a + b = (a + b) mod 7 a - b = (a - b) mod 7 a * b = (a × b) mod 7 a / b = (a × b⁻¹) mod 7 [b≠0].
G#K := E#N - J#O. J#O := 4. E#N := 4. G#K? | Operator definitions (evaluate strictly left to right, all results mod 7): a + b = (a + b) mod 7 a - b = (a - b) mod 7 a * b = (a × b) mod 7 a / b = (a × b⁻¹) mod 7 [b≠0]. | G#K := E#N - J#O. J#O := 4. E#N := 4. | G#K | 0 | E#N = 4 -> E#N = 4
J#O = 4 -> J#O = 4
G#K = E#N - J#O
= 4 - 4
4 - 4 = (4 - 4) mod 7 = 0
=> G#K = 0 | [
{
"glyph": "+",
"kind": "add",
"params": {},
"definition": "a + b = (a + b) mod 7"
},
{
"glyph": "-",
"kind": "sub",
"params": {},
"definition": "a - b = (a - b) mod 7"
},
{
"glyph": "*",
"kind": "mul",
"params": {},
"definition": "a * b = (a × b) mod 7"
},
... | 2 | 2 | 3 | 3 | 0 | {
"E#N": 1,
"J#O": 1,
"G#K": 2
} | mod7_arith_d2_0001 |
7 | arith | Operator definitions (evaluate strictly left to right, all results mod 7): a + b = (a + b) mod 7 a - b = (a - b) mod 7 a * b = (a × b) mod 7 a / b = (a × b⁻¹) mod 7 [b≠0].
G#P := 4. L#L := 4. J#N := 3. L#K := 4. I#P := 5 * L#K - J#N. I#P? | Operator definitions (evaluate strictly left to right, all results mod 7): a + b = (a + b) mod 7 a - b = (a - b) mod 7 a * b = (a × b) mod 7 a / b = (a × b⁻¹) mod 7 [b≠0]. | G#P := 4. L#L := 4. J#N := 3. L#K := 4. I#P := 5 * L#K - J#N. | I#P | 3 | J#N = 3 -> J#N = 3
L#K = 4 -> L#K = 4
I#P = 5 * L#K - J#N
= 5 * 4 - 3
5 * 4 = (5 × 4) mod 7 = 6
6 - 3 = (6 - 3) mod 7 = 3
=> I#P = 3 | [
{
"glyph": "+",
"kind": "add",
"params": {},
"definition": "a + b = (a + b) mod 7"
},
{
"glyph": "-",
"kind": "sub",
"params": {},
"definition": "a - b = (a - b) mod 7"
},
{
"glyph": "*",
"kind": "mul",
"params": {},
"definition": "a * b = (a × b) mod 7"
},
... | 2 | 2 | 5 | 3 | 0 | {
"G#P": 1,
"J#N": 1,
"L#K": 1,
"L#L": 1,
"I#P": 2
} | mod7_arith_d2_0002 |
7 | arith | Operator definitions (evaluate strictly left to right, all results mod 7): a + b = (a + b) mod 7 a - b = (a - b) mod 7 a * b = (a × b) mod 7 a / b = (a × b⁻¹) mod 7 [b≠0].
J#J := 3. E#L := J#J. H#P := 5. K#M := 6. E#L? | Operator definitions (evaluate strictly left to right, all results mod 7): a + b = (a + b) mod 7 a - b = (a - b) mod 7 a * b = (a × b) mod 7 a / b = (a × b⁻¹) mod 7 [b≠0]. | J#J := 3. E#L := J#J. H#P := 5. K#M := 6. | E#L | 3 | J#J = 3 -> J#J = 3
E#L = J#J = 3 | [
{
"glyph": "+",
"kind": "add",
"params": {},
"definition": "a + b = (a + b) mod 7"
},
{
"glyph": "-",
"kind": "sub",
"params": {},
"definition": "a - b = (a - b) mod 7"
},
{
"glyph": "*",
"kind": "mul",
"params": {},
"definition": "a * b = (a × b) mod 7"
},
... | 2 | 2 | 4 | 2 | 0 | {
"K#M": 1,
"H#P": 1,
"J#J": 1,
"E#L": 2
} | mod7_arith_d2_0003 |
7 | arith | Operator definitions (evaluate strictly left to right, all results mod 7): a + b = (a + b) mod 7 a - b = (a - b) mod 7 a * b = (a × b) mod 7 a / b = (a × b⁻¹) mod 7 [b≠0].
J#N := 2. K#I := 1. H#L := 1. H#I := F#K. F#K := 3. H#I? | Operator definitions (evaluate strictly left to right, all results mod 7): a + b = (a + b) mod 7 a - b = (a - b) mod 7 a * b = (a × b) mod 7 a / b = (a × b⁻¹) mod 7 [b≠0]. | J#N := 2. K#I := 1. H#L := 1. H#I := F#K. F#K := 3. | H#I | 3 | F#K = 3 -> F#K = 3
H#I = F#K = 3 | [
{
"glyph": "+",
"kind": "add",
"params": {},
"definition": "a + b = (a + b) mod 7"
},
{
"glyph": "-",
"kind": "sub",
"params": {},
"definition": "a - b = (a - b) mod 7"
},
{
"glyph": "*",
"kind": "mul",
"params": {},
"definition": "a * b = (a × b) mod 7"
},
... | 2 | 2 | 5 | 2 | 0 | {
"F#K": 1,
"H#L": 1,
"K#I": 1,
"J#N": 1,
"H#I": 2
} | mod7_arith_d2_0004 |
7 | arith | Operator definitions (evaluate strictly left to right, all results mod 7): a + b = (a + b) mod 7 a - b = (a - b) mod 7 a * b = (a × b) mod 7 a / b = (a × b⁻¹) mod 7 [b≠0].
E#L := G#K. E#O := 5. G#K := 5. E#L? | Operator definitions (evaluate strictly left to right, all results mod 7): a + b = (a + b) mod 7 a - b = (a - b) mod 7 a * b = (a × b) mod 7 a / b = (a × b⁻¹) mod 7 [b≠0]. | E#L := G#K. E#O := 5. G#K := 5. | E#L | 5 | G#K = 5 -> G#K = 5
E#L = G#K = 5 | [
{
"glyph": "+",
"kind": "add",
"params": {},
"definition": "a + b = (a + b) mod 7"
},
{
"glyph": "-",
"kind": "sub",
"params": {},
"definition": "a - b = (a - b) mod 7"
},
{
"glyph": "*",
"kind": "mul",
"params": {},
"definition": "a * b = (a × b) mod 7"
},
... | 2 | 2 | 3 | 2 | 0 | {
"G#K": 1,
"E#O": 1,
"E#L": 2
} | mod7_arith_d2_0005 |
7 | arith | Operator definitions (evaluate strictly left to right, all results mod 7): a + b = (a + b) mod 7 a - b = (a - b) mod 7 a * b = (a × b) mod 7 a / b = (a × b⁻¹) mod 7 [b≠0].
F#M := 3. I#O := 5. L#I := 3. G#P := 2. F#N := F#M. F#N? | Operator definitions (evaluate strictly left to right, all results mod 7): a + b = (a + b) mod 7 a - b = (a - b) mod 7 a * b = (a × b) mod 7 a / b = (a × b⁻¹) mod 7 [b≠0]. | F#M := 3. I#O := 5. L#I := 3. G#P := 2. F#N := F#M. | F#N | 3 | F#M = 3 -> F#M = 3
F#N = F#M = 3 | [
{
"glyph": "+",
"kind": "add",
"params": {},
"definition": "a + b = (a + b) mod 7"
},
{
"glyph": "-",
"kind": "sub",
"params": {},
"definition": "a - b = (a - b) mod 7"
},
{
"glyph": "*",
"kind": "mul",
"params": {},
"definition": "a * b = (a × b) mod 7"
},
... | 2 | 2 | 5 | 2 | 0 | {
"F#M": 1,
"L#I": 1,
"I#O": 1,
"G#P": 1,
"F#N": 2
} | mod7_arith_d2_0006 |
7 | arith | Operator definitions (evaluate strictly left to right, all results mod 7): a + b = (a + b) mod 7 a - b = (a - b) mod 7 a * b = (a × b) mod 7 a / b = (a × b⁻¹) mod 7 [b≠0].
K#I := 6. G#I := K#I. J#M := 3. G#I? | Operator definitions (evaluate strictly left to right, all results mod 7): a + b = (a + b) mod 7 a - b = (a - b) mod 7 a * b = (a × b) mod 7 a / b = (a × b⁻¹) mod 7 [b≠0]. | K#I := 6. G#I := K#I. J#M := 3. | G#I | 6 | K#I = 6 -> K#I = 6
G#I = K#I = 6 | [
{
"glyph": "+",
"kind": "add",
"params": {},
"definition": "a + b = (a + b) mod 7"
},
{
"glyph": "-",
"kind": "sub",
"params": {},
"definition": "a - b = (a - b) mod 7"
},
{
"glyph": "*",
"kind": "mul",
"params": {},
"definition": "a * b = (a × b) mod 7"
},
... | 2 | 2 | 3 | 2 | 0 | {
"J#M": 1,
"K#I": 1,
"G#I": 2
} | mod7_arith_d2_0007 |
7 | arith | Operator definitions (evaluate strictly left to right, all results mod 7): a + b = (a + b) mod 7 a - b = (a - b) mod 7 a * b = (a × b) mod 7 a / b = (a × b⁻¹) mod 7 [b≠0].
F#P := 6. H#P := H#I * F#P. H#I := 2. H#P? | Operator definitions (evaluate strictly left to right, all results mod 7): a + b = (a + b) mod 7 a - b = (a - b) mod 7 a * b = (a × b) mod 7 a / b = (a × b⁻¹) mod 7 [b≠0]. | F#P := 6. H#P := H#I * F#P. H#I := 2. | H#P | 5 | F#P = 6 -> F#P = 6
H#I = 2 -> H#I = 2
H#P = H#I * F#P
= 2 * 6
2 * 6 = (2 × 6) mod 7 = 5
=> H#P = 5 | [
{
"glyph": "+",
"kind": "add",
"params": {},
"definition": "a + b = (a + b) mod 7"
},
{
"glyph": "-",
"kind": "sub",
"params": {},
"definition": "a - b = (a - b) mod 7"
},
{
"glyph": "*",
"kind": "mul",
"params": {},
"definition": "a * b = (a × b) mod 7"
},
... | 2 | 2 | 3 | 3 | 0 | {
"F#P": 1,
"H#I": 1,
"H#P": 2
} | mod7_arith_d2_0008 |
7 | arith | Operator definitions (evaluate strictly left to right, all results mod 7): a + b = (a + b) mod 7 a - b = (a - b) mod 7 a * b = (a × b) mod 7 a / b = (a × b⁻¹) mod 7 [b≠0].
E#K := 1. F#J := 2. K#O := 2. H#J := E#K. H#J? | Operator definitions (evaluate strictly left to right, all results mod 7): a + b = (a + b) mod 7 a - b = (a - b) mod 7 a * b = (a × b) mod 7 a / b = (a × b⁻¹) mod 7 [b≠0]. | E#K := 1. F#J := 2. K#O := 2. H#J := E#K. | H#J | 1 | E#K = 1 -> E#K = 1
H#J = E#K = 1 | [
{
"glyph": "+",
"kind": "add",
"params": {},
"definition": "a + b = (a + b) mod 7"
},
{
"glyph": "-",
"kind": "sub",
"params": {},
"definition": "a - b = (a - b) mod 7"
},
{
"glyph": "*",
"kind": "mul",
"params": {},
"definition": "a * b = (a × b) mod 7"
},
... | 2 | 2 | 4 | 2 | 0 | {
"E#K": 1,
"K#O": 1,
"F#J": 1,
"H#J": 2
} | mod7_arith_d2_0009 |
7 | arith | Operator definitions (evaluate strictly left to right, all results mod 7): a + b = (a + b) mod 7 a - b = (a - b) mod 7 a * b = (a × b) mod 7 a / b = (a × b⁻¹) mod 7 [b≠0].
H#O := 4. G#J := H#O * E#I. E#I := 4. G#J? | Operator definitions (evaluate strictly left to right, all results mod 7): a + b = (a + b) mod 7 a - b = (a - b) mod 7 a * b = (a × b) mod 7 a / b = (a × b⁻¹) mod 7 [b≠0]. | H#O := 4. G#J := H#O * E#I. E#I := 4. | G#J | 2 | H#O = 4 -> H#O = 4
E#I = 4 -> E#I = 4
G#J = H#O * E#I
= 4 * 4
4 * 4 = (4 × 4) mod 7 = 2
=> G#J = 2 | [
{
"glyph": "+",
"kind": "add",
"params": {},
"definition": "a + b = (a + b) mod 7"
},
{
"glyph": "-",
"kind": "sub",
"params": {},
"definition": "a - b = (a - b) mod 7"
},
{
"glyph": "*",
"kind": "mul",
"params": {},
"definition": "a * b = (a × b) mod 7"
},
... | 2 | 2 | 3 | 3 | 0 | {
"H#O": 1,
"E#I": 1,
"G#J": 2
} | mod7_arith_d2_0010 |
7 | arith | Operator definitions (evaluate strictly left to right, all results mod 7): a + b = (a + b) mod 7 a - b = (a - b) mod 7 a * b = (a × b) mod 7 a / b = (a × b⁻¹) mod 7 [b≠0].
F#M := 2. E#O := 1. K#P := E#O * F#M. E#P := 1. K#P? | Operator definitions (evaluate strictly left to right, all results mod 7): a + b = (a + b) mod 7 a - b = (a - b) mod 7 a * b = (a × b) mod 7 a / b = (a × b⁻¹) mod 7 [b≠0]. | F#M := 2. E#O := 1. K#P := E#O * F#M. E#P := 1. | K#P | 2 | E#O = 1 -> E#O = 1
F#M = 2 -> F#M = 2
K#P = E#O * F#M
= 1 * 2
1 * 2 = (1 × 2) mod 7 = 2
=> K#P = 2 | [
{
"glyph": "+",
"kind": "add",
"params": {},
"definition": "a + b = (a + b) mod 7"
},
{
"glyph": "-",
"kind": "sub",
"params": {},
"definition": "a - b = (a - b) mod 7"
},
{
"glyph": "*",
"kind": "mul",
"params": {},
"definition": "a * b = (a × b) mod 7"
},
... | 2 | 2 | 4 | 3 | 0 | {
"E#O": 1,
"F#M": 1,
"E#P": 1,
"K#P": 2
} | mod7_arith_d2_0011 |
7 | arith | Operator definitions (evaluate strictly left to right, all results mod 7): a + b = (a + b) mod 7 a - b = (a - b) mod 7 a * b = (a × b) mod 7 a / b = (a × b⁻¹) mod 7 [b≠0].
J#O := 6. L#L := 1. L#K := L#L / 4 - J#O. L#K? | Operator definitions (evaluate strictly left to right, all results mod 7): a + b = (a + b) mod 7 a - b = (a - b) mod 7 a * b = (a × b) mod 7 a / b = (a × b⁻¹) mod 7 [b≠0]. | J#O := 6. L#L := 1. L#K := L#L / 4 - J#O. | L#K | 3 | L#L = 1 -> L#L = 1
J#O = 6 -> J#O = 6
L#K = L#L / 4 - J#O
= 1 / 4 - 6
1 / 4 = (1 × 4⁻¹) mod 7 = 2
2 - 6 = (2 - 6) mod 7 = 3
=> L#K = 3 | [
{
"glyph": "+",
"kind": "add",
"params": {},
"definition": "a + b = (a + b) mod 7"
},
{
"glyph": "-",
"kind": "sub",
"params": {},
"definition": "a - b = (a - b) mod 7"
},
{
"glyph": "*",
"kind": "mul",
"params": {},
"definition": "a * b = (a × b) mod 7"
},
... | 2 | 2 | 3 | 3 | 0 | {
"L#L": 1,
"J#O": 1,
"L#K": 2
} | mod7_arith_d2_0012 |
7 | arith | Operator definitions (evaluate strictly left to right, all results mod 7): a + b = (a + b) mod 7 a - b = (a - b) mod 7 a * b = (a × b) mod 7 a / b = (a × b⁻¹) mod 7 [b≠0].
L#I := 6. L#K := L#M / L#I. L#M := 3. L#K? | Operator definitions (evaluate strictly left to right, all results mod 7): a + b = (a + b) mod 7 a - b = (a - b) mod 7 a * b = (a × b) mod 7 a / b = (a × b⁻¹) mod 7 [b≠0]. | L#I := 6. L#K := L#M / L#I. L#M := 3. | L#K | 4 | L#I = 6 -> L#I = 6
L#M = 3 -> L#M = 3
L#K = L#M / L#I
= 3 / 6
3 / 6 = (3 × 6⁻¹) mod 7 = 4
=> L#K = 4 | [
{
"glyph": "+",
"kind": "add",
"params": {},
"definition": "a + b = (a + b) mod 7"
},
{
"glyph": "-",
"kind": "sub",
"params": {},
"definition": "a - b = (a - b) mod 7"
},
{
"glyph": "*",
"kind": "mul",
"params": {},
"definition": "a * b = (a × b) mod 7"
},
... | 2 | 2 | 3 | 3 | 0 | {
"L#I": 1,
"L#M": 1,
"L#K": 2
} | mod7_arith_d2_0013 |
7 | arith | Operator definitions (evaluate strictly left to right, all results mod 7): a + b = (a + b) mod 7 a - b = (a - b) mod 7 a * b = (a × b) mod 7 a / b = (a × b⁻¹) mod 7 [b≠0].
J#K := 2 - F#J. H#K := 4. I#O := 6. F#J := 1. J#K? | Operator definitions (evaluate strictly left to right, all results mod 7): a + b = (a + b) mod 7 a - b = (a - b) mod 7 a * b = (a × b) mod 7 a / b = (a × b⁻¹) mod 7 [b≠0]. | J#K := 2 - F#J. H#K := 4. I#O := 6. F#J := 1. | J#K | 1 | F#J = 1 -> F#J = 1
J#K = 2 - F#J
= 2 - 1
2 - 1 = (2 - 1) mod 7 = 1
=> J#K = 1 | [
{
"glyph": "+",
"kind": "add",
"params": {},
"definition": "a + b = (a + b) mod 7"
},
{
"glyph": "-",
"kind": "sub",
"params": {},
"definition": "a - b = (a - b) mod 7"
},
{
"glyph": "*",
"kind": "mul",
"params": {},
"definition": "a * b = (a × b) mod 7"
},
... | 2 | 2 | 4 | 2 | 0 | {
"H#K": 1,
"I#O": 1,
"F#J": 1,
"J#K": 2
} | mod7_arith_d2_0014 |
7 | arith | Operator definitions (evaluate strictly left to right, all results mod 7): a + b = (a + b) mod 7 a - b = (a - b) mod 7 a * b = (a × b) mod 7 a / b = (a × b⁻¹) mod 7 [b≠0].
J#P := 2. G#P := 6 / I#J + K#J. I#J := 2. K#J := 3. H#M := 2. G#P? | Operator definitions (evaluate strictly left to right, all results mod 7): a + b = (a + b) mod 7 a - b = (a - b) mod 7 a * b = (a × b) mod 7 a / b = (a × b⁻¹) mod 7 [b≠0]. | J#P := 2. G#P := 6 / I#J + K#J. I#J := 2. K#J := 3. H#M := 2. | G#P | 6 | I#J = 2 -> I#J = 2
K#J = 3 -> K#J = 3
G#P = 6 / I#J + K#J
= 6 / 2 + 3
6 / 2 = (6 × 2⁻¹) mod 7 = 3
3 + 3 = (3 + 3) mod 7 = 6
=> G#P = 6 | [
{
"glyph": "+",
"kind": "add",
"params": {},
"definition": "a + b = (a + b) mod 7"
},
{
"glyph": "-",
"kind": "sub",
"params": {},
"definition": "a - b = (a - b) mod 7"
},
{
"glyph": "*",
"kind": "mul",
"params": {},
"definition": "a * b = (a × b) mod 7"
},
... | 2 | 2 | 5 | 3 | 0 | {
"J#P": 1,
"I#J": 1,
"K#J": 1,
"H#M": 1,
"G#P": 2
} | mod7_arith_d2_0015 |
7 | arith | Operator definitions (evaluate strictly left to right, all results mod 7): a + b = (a + b) mod 7 a - b = (a - b) mod 7 a * b = (a × b) mod 7 a / b = (a × b⁻¹) mod 7 [b≠0].
L#P := J#J. H#L := 4. K#P := 3. K#I := 3. J#J := 6. L#P? | Operator definitions (evaluate strictly left to right, all results mod 7): a + b = (a + b) mod 7 a - b = (a - b) mod 7 a * b = (a × b) mod 7 a / b = (a × b⁻¹) mod 7 [b≠0]. | L#P := J#J. H#L := 4. K#P := 3. K#I := 3. J#J := 6. | L#P | 6 | J#J = 6 -> J#J = 6
L#P = J#J = 6 | [
{
"glyph": "+",
"kind": "add",
"params": {},
"definition": "a + b = (a + b) mod 7"
},
{
"glyph": "-",
"kind": "sub",
"params": {},
"definition": "a - b = (a - b) mod 7"
},
{
"glyph": "*",
"kind": "mul",
"params": {},
"definition": "a * b = (a × b) mod 7"
},
... | 2 | 2 | 5 | 2 | 0 | {
"K#P": 1,
"J#J": 1,
"H#L": 1,
"K#I": 1,
"L#P": 2
} | mod7_arith_d2_0016 |
7 | arith | Operator definitions (evaluate strictly left to right, all results mod 7): a + b = (a + b) mod 7 a - b = (a - b) mod 7 a * b = (a × b) mod 7 a / b = (a × b⁻¹) mod 7 [b≠0].
H#P := 5. H#M := 6. G#I := 5. K#P := H#P + 2. K#P? | Operator definitions (evaluate strictly left to right, all results mod 7): a + b = (a + b) mod 7 a - b = (a - b) mod 7 a * b = (a × b) mod 7 a / b = (a × b⁻¹) mod 7 [b≠0]. | H#P := 5. H#M := 6. G#I := 5. K#P := H#P + 2. | K#P | 0 | H#P = 5 -> H#P = 5
K#P = H#P + 2
= 5 + 2
5 + 2 = (5 + 2) mod 7 = 0
=> K#P = 0 | [
{
"glyph": "+",
"kind": "add",
"params": {},
"definition": "a + b = (a + b) mod 7"
},
{
"glyph": "-",
"kind": "sub",
"params": {},
"definition": "a - b = (a - b) mod 7"
},
{
"glyph": "*",
"kind": "mul",
"params": {},
"definition": "a * b = (a × b) mod 7"
},
... | 2 | 2 | 4 | 2 | 0 | {
"H#M": 1,
"H#P": 1,
"G#I": 1,
"K#P": 2
} | mod7_arith_d2_0017 |
7 | arith | Operator definitions (evaluate strictly left to right, all results mod 7): a + b = (a + b) mod 7 a - b = (a - b) mod 7 a * b = (a × b) mod 7 a / b = (a × b⁻¹) mod 7 [b≠0].
G#I := I#P + K#M * F#N. I#P := 1. F#N := 2. K#M := 6. L#N := 4. G#I? | Operator definitions (evaluate strictly left to right, all results mod 7): a + b = (a + b) mod 7 a - b = (a - b) mod 7 a * b = (a × b) mod 7 a / b = (a × b⁻¹) mod 7 [b≠0]. | G#I := I#P + K#M * F#N. I#P := 1. F#N := 2. K#M := 6. L#N := 4. | G#I | 0 | I#P = 1 -> I#P = 1
F#N = 2 -> F#N = 2
K#M = 6 -> K#M = 6
G#I = I#P + K#M * F#N
= 1 + 6 * 2
1 + 6 = (1 + 6) mod 7 = 0
0 * 2 = (0 × 2) mod 7 = 0
=> G#I = 0 | [
{
"glyph": "+",
"kind": "add",
"params": {},
"definition": "a + b = (a + b) mod 7"
},
{
"glyph": "-",
"kind": "sub",
"params": {},
"definition": "a - b = (a - b) mod 7"
},
{
"glyph": "*",
"kind": "mul",
"params": {},
"definition": "a * b = (a × b) mod 7"
},
... | 2 | 2 | 5 | 4 | 0 | {
"L#N": 1,
"I#P": 1,
"F#N": 1,
"K#M": 1,
"G#I": 2
} | mod7_arith_d2_0018 |
7 | arith | Operator definitions (evaluate strictly left to right, all results mod 7): a + b = (a + b) mod 7 a - b = (a - b) mod 7 a * b = (a × b) mod 7 a / b = (a × b⁻¹) mod 7 [b≠0].
G#P := 6. I#P := 6. I#J := G#P / I#P. I#J? | Operator definitions (evaluate strictly left to right, all results mod 7): a + b = (a + b) mod 7 a - b = (a - b) mod 7 a * b = (a × b) mod 7 a / b = (a × b⁻¹) mod 7 [b≠0]. | G#P := 6. I#P := 6. I#J := G#P / I#P. | I#J | 1 | I#P = 6 -> I#P = 6
G#P = 6 -> G#P = 6
I#J = G#P / I#P
= 6 / 6
6 / 6 = (6 × 6⁻¹) mod 7 = 1
=> I#J = 1 | [
{
"glyph": "+",
"kind": "add",
"params": {},
"definition": "a + b = (a + b) mod 7"
},
{
"glyph": "-",
"kind": "sub",
"params": {},
"definition": "a - b = (a - b) mod 7"
},
{
"glyph": "*",
"kind": "mul",
"params": {},
"definition": "a * b = (a × b) mod 7"
},
... | 2 | 2 | 3 | 3 | 0 | {
"I#P": 1,
"G#P": 1,
"I#J": 2
} | mod7_arith_d2_0019 |
7 | arith | Operator definitions (evaluate strictly left to right, all results mod 7): a + b = (a + b) mod 7 a - b = (a - b) mod 7 a * b = (a × b) mod 7 a / b = (a × b⁻¹) mod 7 [b≠0].
H#O := 5. F#J := H#M / H#O. H#M := 1. G#J := 3. E#L := 4. F#J? | Operator definitions (evaluate strictly left to right, all results mod 7): a + b = (a + b) mod 7 a - b = (a - b) mod 7 a * b = (a × b) mod 7 a / b = (a × b⁻¹) mod 7 [b≠0]. | H#O := 5. F#J := H#M / H#O. H#M := 1. G#J := 3. E#L := 4. | F#J | 3 | H#O = 5 -> H#O = 5
H#M = 1 -> H#M = 1
F#J = H#M / H#O
= 1 / 5
1 / 5 = (1 × 5⁻¹) mod 7 = 3
=> F#J = 3 | [
{
"glyph": "+",
"kind": "add",
"params": {},
"definition": "a + b = (a + b) mod 7"
},
{
"glyph": "-",
"kind": "sub",
"params": {},
"definition": "a - b = (a - b) mod 7"
},
{
"glyph": "*",
"kind": "mul",
"params": {},
"definition": "a * b = (a × b) mod 7"
},
... | 2 | 2 | 5 | 3 | 0 | {
"H#O": 1,
"G#J": 1,
"E#L": 1,
"H#M": 1,
"F#J": 2
} | mod7_arith_d2_0020 |
7 | arith | Operator definitions (evaluate strictly left to right, all results mod 7): a + b = (a + b) mod 7 a - b = (a - b) mod 7 a * b = (a × b) mod 7 a / b = (a × b⁻¹) mod 7 [b≠0].
L#K := 6. L#L := 3. H#P := L#L - L#K. J#K := 1. H#P? | Operator definitions (evaluate strictly left to right, all results mod 7): a + b = (a + b) mod 7 a - b = (a - b) mod 7 a * b = (a × b) mod 7 a / b = (a × b⁻¹) mod 7 [b≠0]. | L#K := 6. L#L := 3. H#P := L#L - L#K. J#K := 1. | H#P | 4 | L#K = 6 -> L#K = 6
L#L = 3 -> L#L = 3
H#P = L#L - L#K
= 3 - 6
3 - 6 = (3 - 6) mod 7 = 4
=> H#P = 4 | [
{
"glyph": "+",
"kind": "add",
"params": {},
"definition": "a + b = (a + b) mod 7"
},
{
"glyph": "-",
"kind": "sub",
"params": {},
"definition": "a - b = (a - b) mod 7"
},
{
"glyph": "*",
"kind": "mul",
"params": {},
"definition": "a * b = (a × b) mod 7"
},
... | 2 | 2 | 4 | 3 | 0 | {
"L#K": 1,
"L#L": 1,
"J#K": 1,
"H#P": 2
} | mod7_arith_d2_0021 |
7 | arith | Operator definitions (evaluate strictly left to right, all results mod 7): a + b = (a + b) mod 7 a - b = (a - b) mod 7 a * b = (a × b) mod 7 a / b = (a × b⁻¹) mod 7 [b≠0].
I#J := 3. J#O := 6. I#O := J#O / 4. J#M := 6. I#O? | Operator definitions (evaluate strictly left to right, all results mod 7): a + b = (a + b) mod 7 a - b = (a - b) mod 7 a * b = (a × b) mod 7 a / b = (a × b⁻¹) mod 7 [b≠0]. | I#J := 3. J#O := 6. I#O := J#O / 4. J#M := 6. | I#O | 5 | J#O = 6 -> J#O = 6
I#O = J#O / 4
= 6 / 4
6 / 4 = (6 × 4⁻¹) mod 7 = 5
=> I#O = 5 | [
{
"glyph": "+",
"kind": "add",
"params": {},
"definition": "a + b = (a + b) mod 7"
},
{
"glyph": "-",
"kind": "sub",
"params": {},
"definition": "a - b = (a - b) mod 7"
},
{
"glyph": "*",
"kind": "mul",
"params": {},
"definition": "a * b = (a × b) mod 7"
},
... | 2 | 2 | 4 | 2 | 0 | {
"J#M": 1,
"J#O": 1,
"I#J": 1,
"I#O": 2
} | mod7_arith_d2_0022 |
7 | arith | Operator definitions (evaluate strictly left to right, all results mod 7): a + b = (a + b) mod 7 a - b = (a - b) mod 7 a * b = (a × b) mod 7 a / b = (a × b⁻¹) mod 7 [b≠0].
F#O := 1. J#L := 4 / F#O + J#K. G#I := 1. J#K := 3. J#L? | Operator definitions (evaluate strictly left to right, all results mod 7): a + b = (a + b) mod 7 a - b = (a - b) mod 7 a * b = (a × b) mod 7 a / b = (a × b⁻¹) mod 7 [b≠0]. | F#O := 1. J#L := 4 / F#O + J#K. G#I := 1. J#K := 3. | J#L | 0 | J#K = 3 -> J#K = 3
F#O = 1 -> F#O = 1
J#L = 4 / F#O + J#K
= 4 / 1 + 3
4 / 1 = (4 × 1⁻¹) mod 7 = 4
4 + 3 = (4 + 3) mod 7 = 0
=> J#L = 0 | [
{
"glyph": "+",
"kind": "add",
"params": {},
"definition": "a + b = (a + b) mod 7"
},
{
"glyph": "-",
"kind": "sub",
"params": {},
"definition": "a - b = (a - b) mod 7"
},
{
"glyph": "*",
"kind": "mul",
"params": {},
"definition": "a * b = (a × b) mod 7"
},
... | 2 | 2 | 4 | 3 | 0 | {
"G#I": 1,
"J#K": 1,
"F#O": 1,
"J#L": 2
} | mod7_arith_d2_0023 |
7 | arith | Operator definitions (evaluate strictly left to right, all results mod 7): a + b = (a + b) mod 7 a - b = (a - b) mod 7 a * b = (a × b) mod 7 a / b = (a × b⁻¹) mod 7 [b≠0].
H#L := 6. G#O := 3. I#J := 3. H#I := 3 / I#J. H#I? | Operator definitions (evaluate strictly left to right, all results mod 7): a + b = (a + b) mod 7 a - b = (a - b) mod 7 a * b = (a × b) mod 7 a / b = (a × b⁻¹) mod 7 [b≠0]. | H#L := 6. G#O := 3. I#J := 3. H#I := 3 / I#J. | H#I | 1 | I#J = 3 -> I#J = 3
H#I = 3 / I#J
= 3 / 3
3 / 3 = (3 × 3⁻¹) mod 7 = 1
=> H#I = 1 | [
{
"glyph": "+",
"kind": "add",
"params": {},
"definition": "a + b = (a + b) mod 7"
},
{
"glyph": "-",
"kind": "sub",
"params": {},
"definition": "a - b = (a - b) mod 7"
},
{
"glyph": "*",
"kind": "mul",
"params": {},
"definition": "a * b = (a × b) mod 7"
},
... | 2 | 2 | 4 | 2 | 0 | {
"G#O": 1,
"I#J": 1,
"H#L": 1,
"H#I": 2
} | mod7_arith_d2_0024 |
7 | arith | Operator definitions (evaluate strictly left to right, all results mod 7): a + b = (a + b) mod 7 a - b = (a - b) mod 7 a * b = (a × b) mod 7 a / b = (a × b⁻¹) mod 7 [b≠0].
K#L := 1. F#N := 6. K#P := 4. J#J := K#P + K#L + 5. J#J? | Operator definitions (evaluate strictly left to right, all results mod 7): a + b = (a + b) mod 7 a - b = (a - b) mod 7 a * b = (a × b) mod 7 a / b = (a × b⁻¹) mod 7 [b≠0]. | K#L := 1. F#N := 6. K#P := 4. J#J := K#P + K#L + 5. | J#J | 3 | K#L = 1 -> K#L = 1
K#P = 4 -> K#P = 4
J#J = K#P + K#L + 5
= 4 + 1 + 5
4 + 1 = (4 + 1) mod 7 = 5
5 + 5 = (5 + 5) mod 7 = 3
=> J#J = 3 | [
{
"glyph": "+",
"kind": "add",
"params": {},
"definition": "a + b = (a + b) mod 7"
},
{
"glyph": "-",
"kind": "sub",
"params": {},
"definition": "a - b = (a - b) mod 7"
},
{
"glyph": "*",
"kind": "mul",
"params": {},
"definition": "a * b = (a × b) mod 7"
},
... | 2 | 2 | 4 | 3 | 0 | {
"F#N": 1,
"K#L": 1,
"K#P": 1,
"J#J": 2
} | mod7_arith_d2_0025 |
7 | arith | Operator definitions (evaluate strictly left to right, all results mod 7): a + b = (a + b) mod 7 a - b = (a - b) mod 7 a * b = (a × b) mod 7 a / b = (a × b⁻¹) mod 7 [b≠0].
E#M := I#P - G#J. G#J := 4. I#P := 6. E#M? | Operator definitions (evaluate strictly left to right, all results mod 7): a + b = (a + b) mod 7 a - b = (a - b) mod 7 a * b = (a × b) mod 7 a / b = (a × b⁻¹) mod 7 [b≠0]. | E#M := I#P - G#J. G#J := 4. I#P := 6. | E#M | 2 | G#J = 4 -> G#J = 4
I#P = 6 -> I#P = 6
E#M = I#P - G#J
= 6 - 4
6 - 4 = (6 - 4) mod 7 = 2
=> E#M = 2 | [
{
"glyph": "+",
"kind": "add",
"params": {},
"definition": "a + b = (a + b) mod 7"
},
{
"glyph": "-",
"kind": "sub",
"params": {},
"definition": "a - b = (a - b) mod 7"
},
{
"glyph": "*",
"kind": "mul",
"params": {},
"definition": "a * b = (a × b) mod 7"
},
... | 2 | 2 | 3 | 3 | 0 | {
"G#J": 1,
"I#P": 1,
"E#M": 2
} | mod7_arith_d2_0026 |
7 | arith | Operator definitions (evaluate strictly left to right, all results mod 7): a + b = (a + b) mod 7 a - b = (a - b) mod 7 a * b = (a × b) mod 7 a / b = (a × b⁻¹) mod 7 [b≠0].
G#I := 2. E#I := L#I. L#I := 4. H#J := 4. E#I? | Operator definitions (evaluate strictly left to right, all results mod 7): a + b = (a + b) mod 7 a - b = (a - b) mod 7 a * b = (a × b) mod 7 a / b = (a × b⁻¹) mod 7 [b≠0]. | G#I := 2. E#I := L#I. L#I := 4. H#J := 4. | E#I | 4 | L#I = 4 -> L#I = 4
E#I = L#I = 4 | [
{
"glyph": "+",
"kind": "add",
"params": {},
"definition": "a + b = (a + b) mod 7"
},
{
"glyph": "-",
"kind": "sub",
"params": {},
"definition": "a - b = (a - b) mod 7"
},
{
"glyph": "*",
"kind": "mul",
"params": {},
"definition": "a * b = (a × b) mod 7"
},
... | 2 | 2 | 4 | 2 | 0 | {
"L#I": 1,
"H#J": 1,
"G#I": 1,
"E#I": 2
} | mod7_arith_d2_0027 |
7 | arith | Operator definitions (evaluate strictly left to right, all results mod 7): a + b = (a + b) mod 7 a - b = (a - b) mod 7 a * b = (a × b) mod 7 a / b = (a × b⁻¹) mod 7 [b≠0].
E#K := 5. L#L := 1. H#O := E#K - F#L / 3. F#L := 1. H#O? | Operator definitions (evaluate strictly left to right, all results mod 7): a + b = (a + b) mod 7 a - b = (a - b) mod 7 a * b = (a × b) mod 7 a / b = (a × b⁻¹) mod 7 [b≠0]. | E#K := 5. L#L := 1. H#O := E#K - F#L / 3. F#L := 1. | H#O | 6 | E#K = 5 -> E#K = 5
F#L = 1 -> F#L = 1
H#O = E#K - F#L / 3
= 5 - 1 / 3
5 - 1 = (5 - 1) mod 7 = 4
4 / 3 = (4 × 3⁻¹) mod 7 = 6
=> H#O = 6 | [
{
"glyph": "+",
"kind": "add",
"params": {},
"definition": "a + b = (a + b) mod 7"
},
{
"glyph": "-",
"kind": "sub",
"params": {},
"definition": "a - b = (a - b) mod 7"
},
{
"glyph": "*",
"kind": "mul",
"params": {},
"definition": "a * b = (a × b) mod 7"
},
... | 2 | 2 | 4 | 3 | 0 | {
"E#K": 1,
"F#L": 1,
"L#L": 1,
"H#O": 2
} | mod7_arith_d2_0028 |
7 | arith | Operator definitions (evaluate strictly left to right, all results mod 7): a + b = (a + b) mod 7 a - b = (a - b) mod 7 a * b = (a × b) mod 7 a / b = (a × b⁻¹) mod 7 [b≠0].
F#J := 4. I#M := K#N + F#J - 6. G#O := 2. K#N := 3. I#M? | Operator definitions (evaluate strictly left to right, all results mod 7): a + b = (a + b) mod 7 a - b = (a - b) mod 7 a * b = (a × b) mod 7 a / b = (a × b⁻¹) mod 7 [b≠0]. | F#J := 4. I#M := K#N + F#J - 6. G#O := 2. K#N := 3. | I#M | 1 | K#N = 3 -> K#N = 3
F#J = 4 -> F#J = 4
I#M = K#N + F#J - 6
= 3 + 4 - 6
3 + 4 = (3 + 4) mod 7 = 0
0 - 6 = (0 - 6) mod 7 = 1
=> I#M = 1 | [
{
"glyph": "+",
"kind": "add",
"params": {},
"definition": "a + b = (a + b) mod 7"
},
{
"glyph": "-",
"kind": "sub",
"params": {},
"definition": "a - b = (a - b) mod 7"
},
{
"glyph": "*",
"kind": "mul",
"params": {},
"definition": "a * b = (a × b) mod 7"
},
... | 2 | 2 | 4 | 3 | 0 | {
"G#O": 1,
"K#N": 1,
"F#J": 1,
"I#M": 2
} | mod7_arith_d2_0029 |
7 | arith | Operator definitions (evaluate strictly left to right, all results mod 7): a + b = (a + b) mod 7 a - b = (a - b) mod 7 a * b = (a × b) mod 7 a / b = (a × b⁻¹) mod 7 [b≠0].
J#I := E#M. E#M := 6. L#I := 6. H#K := 5. E#K := 6. J#I? | Operator definitions (evaluate strictly left to right, all results mod 7): a + b = (a + b) mod 7 a - b = (a - b) mod 7 a * b = (a × b) mod 7 a / b = (a × b⁻¹) mod 7 [b≠0]. | J#I := E#M. E#M := 6. L#I := 6. H#K := 5. E#K := 6. | J#I | 6 | E#M = 6 -> E#M = 6
J#I = E#M = 6 | [
{
"glyph": "+",
"kind": "add",
"params": {},
"definition": "a + b = (a + b) mod 7"
},
{
"glyph": "-",
"kind": "sub",
"params": {},
"definition": "a - b = (a - b) mod 7"
},
{
"glyph": "*",
"kind": "mul",
"params": {},
"definition": "a * b = (a × b) mod 7"
},
... | 2 | 2 | 5 | 2 | 0 | {
"E#K": 1,
"E#M": 1,
"L#I": 1,
"H#K": 1,
"J#I": 2
} | mod7_arith_d2_0030 |
7 | arith | Operator definitions (evaluate strictly left to right, all results mod 7): a + b = (a + b) mod 7 a - b = (a - b) mod 7 a * b = (a × b) mod 7 a / b = (a × b⁻¹) mod 7 [b≠0].
I#J := 4. K#I := G#N * I#J. G#N := 6. K#I? | Operator definitions (evaluate strictly left to right, all results mod 7): a + b = (a + b) mod 7 a - b = (a - b) mod 7 a * b = (a × b) mod 7 a / b = (a × b⁻¹) mod 7 [b≠0]. | I#J := 4. K#I := G#N * I#J. G#N := 6. | K#I | 3 | G#N = 6 -> G#N = 6
I#J = 4 -> I#J = 4
K#I = G#N * I#J
= 6 * 4
6 * 4 = (6 × 4) mod 7 = 3
=> K#I = 3 | [
{
"glyph": "+",
"kind": "add",
"params": {},
"definition": "a + b = (a + b) mod 7"
},
{
"glyph": "-",
"kind": "sub",
"params": {},
"definition": "a - b = (a - b) mod 7"
},
{
"glyph": "*",
"kind": "mul",
"params": {},
"definition": "a * b = (a × b) mod 7"
},
... | 2 | 2 | 3 | 3 | 0 | {
"G#N": 1,
"I#J": 1,
"K#I": 2
} | mod7_arith_d2_0031 |
7 | arith | Operator definitions (evaluate strictly left to right, all results mod 7): a + b = (a + b) mod 7 a - b = (a - b) mod 7 a * b = (a × b) mod 7 a / b = (a × b⁻¹) mod 7 [b≠0].
K#L := 4. L#N := J#M / K#L * G#K. J#M := 5. G#K := 4. L#N? | Operator definitions (evaluate strictly left to right, all results mod 7): a + b = (a + b) mod 7 a - b = (a - b) mod 7 a * b = (a × b) mod 7 a / b = (a × b⁻¹) mod 7 [b≠0]. | K#L := 4. L#N := J#M / K#L * G#K. J#M := 5. G#K := 4. | L#N | 5 | J#M = 5 -> J#M = 5
K#L = 4 -> K#L = 4
G#K = 4 -> G#K = 4
L#N = J#M / K#L * G#K
= 5 / 4 * 4
5 / 4 = (5 × 4⁻¹) mod 7 = 3
3 * 4 = (3 × 4) mod 7 = 5
=> L#N = 5 | [
{
"glyph": "+",
"kind": "add",
"params": {},
"definition": "a + b = (a + b) mod 7"
},
{
"glyph": "-",
"kind": "sub",
"params": {},
"definition": "a - b = (a - b) mod 7"
},
{
"glyph": "*",
"kind": "mul",
"params": {},
"definition": "a * b = (a × b) mod 7"
},
... | 2 | 2 | 4 | 4 | 0 | {
"J#M": 1,
"K#L": 1,
"G#K": 1,
"L#N": 2
} | mod7_arith_d2_0032 |
7 | arith | Operator definitions (evaluate strictly left to right, all results mod 7): a + b = (a + b) mod 7 a - b = (a - b) mod 7 a * b = (a × b) mod 7 a / b = (a × b⁻¹) mod 7 [b≠0].
L#L := 5. G#M := 2. E#L := G#M. I#J := 1. E#L? | Operator definitions (evaluate strictly left to right, all results mod 7): a + b = (a + b) mod 7 a - b = (a - b) mod 7 a * b = (a × b) mod 7 a / b = (a × b⁻¹) mod 7 [b≠0]. | L#L := 5. G#M := 2. E#L := G#M. I#J := 1. | E#L | 2 | G#M = 2 -> G#M = 2
E#L = G#M = 2 | [
{
"glyph": "+",
"kind": "add",
"params": {},
"definition": "a + b = (a + b) mod 7"
},
{
"glyph": "-",
"kind": "sub",
"params": {},
"definition": "a - b = (a - b) mod 7"
},
{
"glyph": "*",
"kind": "mul",
"params": {},
"definition": "a * b = (a × b) mod 7"
},
... | 2 | 2 | 4 | 2 | 0 | {
"L#L": 1,
"G#M": 1,
"I#J": 1,
"E#L": 2
} | mod7_arith_d2_0033 |
7 | arith | Operator definitions (evaluate strictly left to right, all results mod 7): a + b = (a + b) mod 7 a - b = (a - b) mod 7 a * b = (a × b) mod 7 a / b = (a × b⁻¹) mod 7 [b≠0].
E#M := 5. F#O := 4. G#O := G#L. G#L := 2. G#O? | Operator definitions (evaluate strictly left to right, all results mod 7): a + b = (a + b) mod 7 a - b = (a - b) mod 7 a * b = (a × b) mod 7 a / b = (a × b⁻¹) mod 7 [b≠0]. | E#M := 5. F#O := 4. G#O := G#L. G#L := 2. | G#O | 2 | G#L = 2 -> G#L = 2
G#O = G#L = 2 | [
{
"glyph": "+",
"kind": "add",
"params": {},
"definition": "a + b = (a + b) mod 7"
},
{
"glyph": "-",
"kind": "sub",
"params": {},
"definition": "a - b = (a - b) mod 7"
},
{
"glyph": "*",
"kind": "mul",
"params": {},
"definition": "a * b = (a × b) mod 7"
},
... | 2 | 2 | 4 | 2 | 0 | {
"F#O": 1,
"E#M": 1,
"G#L": 1,
"G#O": 2
} | mod7_arith_d2_0034 |
7 | arith | Operator definitions (evaluate strictly left to right, all results mod 7): a + b = (a + b) mod 7 a - b = (a - b) mod 7 a * b = (a × b) mod 7 a / b = (a × b⁻¹) mod 7 [b≠0].
J#O := 5. L#L := 2. I#L := 2. K#L := L#L - J#O. K#L? | Operator definitions (evaluate strictly left to right, all results mod 7): a + b = (a + b) mod 7 a - b = (a - b) mod 7 a * b = (a × b) mod 7 a / b = (a × b⁻¹) mod 7 [b≠0]. | J#O := 5. L#L := 2. I#L := 2. K#L := L#L - J#O. | K#L | 4 | L#L = 2 -> L#L = 2
J#O = 5 -> J#O = 5
K#L = L#L - J#O
= 2 - 5
2 - 5 = (2 - 5) mod 7 = 4
=> K#L = 4 | [
{
"glyph": "+",
"kind": "add",
"params": {},
"definition": "a + b = (a + b) mod 7"
},
{
"glyph": "-",
"kind": "sub",
"params": {},
"definition": "a - b = (a - b) mod 7"
},
{
"glyph": "*",
"kind": "mul",
"params": {},
"definition": "a * b = (a × b) mod 7"
},
... | 2 | 2 | 4 | 3 | 0 | {
"L#L": 1,
"I#L": 1,
"J#O": 1,
"K#L": 2
} | mod7_arith_d2_0035 |
7 | arith | Operator definitions (evaluate strictly left to right, all results mod 7): a + b = (a + b) mod 7 a - b = (a - b) mod 7 a * b = (a × b) mod 7 a / b = (a × b⁻¹) mod 7 [b≠0].
F#I := K#M * H#L / K#O. K#M := 2. H#L := 1. K#O := 4. F#I? | Operator definitions (evaluate strictly left to right, all results mod 7): a + b = (a + b) mod 7 a - b = (a - b) mod 7 a * b = (a × b) mod 7 a / b = (a × b⁻¹) mod 7 [b≠0]. | F#I := K#M * H#L / K#O. K#M := 2. H#L := 1. K#O := 4. | F#I | 4 | K#O = 4 -> K#O = 4
K#M = 2 -> K#M = 2
H#L = 1 -> H#L = 1
F#I = K#M * H#L / K#O
= 2 * 1 / 4
2 * 1 = (2 × 1) mod 7 = 2
2 / 4 = (2 × 4⁻¹) mod 7 = 4
=> F#I = 4 | [
{
"glyph": "+",
"kind": "add",
"params": {},
"definition": "a + b = (a + b) mod 7"
},
{
"glyph": "-",
"kind": "sub",
"params": {},
"definition": "a - b = (a - b) mod 7"
},
{
"glyph": "*",
"kind": "mul",
"params": {},
"definition": "a * b = (a × b) mod 7"
},
... | 2 | 2 | 4 | 4 | 0 | {
"K#O": 1,
"K#M": 1,
"H#L": 1,
"F#I": 2
} | mod7_arith_d2_0036 |
7 | arith | Operator definitions (evaluate strictly left to right, all results mod 7): a + b = (a + b) mod 7 a - b = (a - b) mod 7 a * b = (a × b) mod 7 a / b = (a × b⁻¹) mod 7 [b≠0].
E#K := G#K. H#M := 1. G#K := 2. J#L := 5. E#P := 1. E#K? | Operator definitions (evaluate strictly left to right, all results mod 7): a + b = (a + b) mod 7 a - b = (a - b) mod 7 a * b = (a × b) mod 7 a / b = (a × b⁻¹) mod 7 [b≠0]. | E#K := G#K. H#M := 1. G#K := 2. J#L := 5. E#P := 1. | E#K | 2 | G#K = 2 -> G#K = 2
E#K = G#K = 2 | [
{
"glyph": "+",
"kind": "add",
"params": {},
"definition": "a + b = (a + b) mod 7"
},
{
"glyph": "-",
"kind": "sub",
"params": {},
"definition": "a - b = (a - b) mod 7"
},
{
"glyph": "*",
"kind": "mul",
"params": {},
"definition": "a * b = (a × b) mod 7"
},
... | 2 | 2 | 5 | 2 | 0 | {
"H#M": 1,
"E#P": 1,
"G#K": 1,
"J#L": 1,
"E#K": 2
} | mod7_arith_d2_0037 |
7 | arith | Operator definitions (evaluate strictly left to right, all results mod 7): a + b = (a + b) mod 7 a - b = (a - b) mod 7 a * b = (a × b) mod 7 a / b = (a × b⁻¹) mod 7 [b≠0].
F#N := I#M / E#N. I#M := 4. E#N := 3. F#N? | Operator definitions (evaluate strictly left to right, all results mod 7): a + b = (a + b) mod 7 a - b = (a - b) mod 7 a * b = (a × b) mod 7 a / b = (a × b⁻¹) mod 7 [b≠0]. | F#N := I#M / E#N. I#M := 4. E#N := 3. | F#N | 6 | I#M = 4 -> I#M = 4
E#N = 3 -> E#N = 3
F#N = I#M / E#N
= 4 / 3
4 / 3 = (4 × 3⁻¹) mod 7 = 6
=> F#N = 6 | [
{
"glyph": "+",
"kind": "add",
"params": {},
"definition": "a + b = (a + b) mod 7"
},
{
"glyph": "-",
"kind": "sub",
"params": {},
"definition": "a - b = (a - b) mod 7"
},
{
"glyph": "*",
"kind": "mul",
"params": {},
"definition": "a * b = (a × b) mod 7"
},
... | 2 | 2 | 3 | 3 | 0 | {
"I#M": 1,
"E#N": 1,
"F#N": 2
} | mod7_arith_d2_0038 |
7 | arith | Operator definitions (evaluate strictly left to right, all results mod 7): a + b = (a + b) mod 7 a - b = (a - b) mod 7 a * b = (a × b) mod 7 a / b = (a × b⁻¹) mod 7 [b≠0].
E#N := 4. E#J := 6. K#O := 3 + E#J. K#O? | Operator definitions (evaluate strictly left to right, all results mod 7): a + b = (a + b) mod 7 a - b = (a - b) mod 7 a * b = (a × b) mod 7 a / b = (a × b⁻¹) mod 7 [b≠0]. | E#N := 4. E#J := 6. K#O := 3 + E#J. | K#O | 2 | E#J = 6 -> E#J = 6
K#O = 3 + E#J
= 3 + 6
3 + 6 = (3 + 6) mod 7 = 2
=> K#O = 2 | [
{
"glyph": "+",
"kind": "add",
"params": {},
"definition": "a + b = (a + b) mod 7"
},
{
"glyph": "-",
"kind": "sub",
"params": {},
"definition": "a - b = (a - b) mod 7"
},
{
"glyph": "*",
"kind": "mul",
"params": {},
"definition": "a * b = (a × b) mod 7"
},
... | 2 | 2 | 3 | 2 | 0 | {
"E#N": 1,
"E#J": 1,
"K#O": 2
} | mod7_arith_d2_0039 |
7 | arith | Operator definitions (evaluate strictly left to right, all results mod 7): a + b = (a + b) mod 7 a - b = (a - b) mod 7 a * b = (a × b) mod 7 a / b = (a × b⁻¹) mod 7 [b≠0].
H#O := 1. J#J := 5. G#M := 1. E#L := 5. F#L := G#M * E#L. F#L? | Operator definitions (evaluate strictly left to right, all results mod 7): a + b = (a + b) mod 7 a - b = (a - b) mod 7 a * b = (a × b) mod 7 a / b = (a × b⁻¹) mod 7 [b≠0]. | H#O := 1. J#J := 5. G#M := 1. E#L := 5. F#L := G#M * E#L. | F#L | 5 | G#M = 1 -> G#M = 1
E#L = 5 -> E#L = 5
F#L = G#M * E#L
= 1 * 5
1 * 5 = (1 × 5) mod 7 = 5
=> F#L = 5 | [
{
"glyph": "+",
"kind": "add",
"params": {},
"definition": "a + b = (a + b) mod 7"
},
{
"glyph": "-",
"kind": "sub",
"params": {},
"definition": "a - b = (a - b) mod 7"
},
{
"glyph": "*",
"kind": "mul",
"params": {},
"definition": "a * b = (a × b) mod 7"
},
... | 2 | 2 | 5 | 3 | 0 | {
"G#M": 1,
"E#L": 1,
"H#O": 1,
"J#J": 1,
"F#L": 2
} | mod7_arith_d2_0040 |
7 | arith | Operator definitions (evaluate strictly left to right, all results mod 7): a + b = (a + b) mod 7 a - b = (a - b) mod 7 a * b = (a × b) mod 7 a / b = (a × b⁻¹) mod 7 [b≠0].
G#K := 4. K#P := 3 - G#K / G#P. G#P := 6. J#I := 5. K#P? | Operator definitions (evaluate strictly left to right, all results mod 7): a + b = (a + b) mod 7 a - b = (a - b) mod 7 a * b = (a × b) mod 7 a / b = (a × b⁻¹) mod 7 [b≠0]. | G#K := 4. K#P := 3 - G#K / G#P. G#P := 6. J#I := 5. | K#P | 1 | G#K = 4 -> G#K = 4
G#P = 6 -> G#P = 6
K#P = 3 - G#K / G#P
= 3 - 4 / 6
3 - 4 = (3 - 4) mod 7 = 6
6 / 6 = (6 × 6⁻¹) mod 7 = 1
=> K#P = 1 | [
{
"glyph": "+",
"kind": "add",
"params": {},
"definition": "a + b = (a + b) mod 7"
},
{
"glyph": "-",
"kind": "sub",
"params": {},
"definition": "a - b = (a - b) mod 7"
},
{
"glyph": "*",
"kind": "mul",
"params": {},
"definition": "a * b = (a × b) mod 7"
},
... | 2 | 2 | 4 | 3 | 0 | {
"G#K": 1,
"G#P": 1,
"J#I": 1,
"K#P": 2
} | mod7_arith_d2_0041 |
7 | arith | Operator definitions (evaluate strictly left to right, all results mod 7): a + b = (a + b) mod 7 a - b = (a - b) mod 7 a * b = (a × b) mod 7 a / b = (a × b⁻¹) mod 7 [b≠0].
I#I := E#O * I#L / H#O. H#O := 4. E#O := 5. I#L := 3. I#I? | Operator definitions (evaluate strictly left to right, all results mod 7): a + b = (a + b) mod 7 a - b = (a - b) mod 7 a * b = (a × b) mod 7 a / b = (a × b⁻¹) mod 7 [b≠0]. | I#I := E#O * I#L / H#O. H#O := 4. E#O := 5. I#L := 3. | I#I | 2 | H#O = 4 -> H#O = 4
I#L = 3 -> I#L = 3
E#O = 5 -> E#O = 5
I#I = E#O * I#L / H#O
= 5 * 3 / 4
5 * 3 = (5 × 3) mod 7 = 1
1 / 4 = (1 × 4⁻¹) mod 7 = 2
=> I#I = 2 | [
{
"glyph": "+",
"kind": "add",
"params": {},
"definition": "a + b = (a + b) mod 7"
},
{
"glyph": "-",
"kind": "sub",
"params": {},
"definition": "a - b = (a - b) mod 7"
},
{
"glyph": "*",
"kind": "mul",
"params": {},
"definition": "a * b = (a × b) mod 7"
},
... | 2 | 2 | 4 | 4 | 0 | {
"H#O": 1,
"I#L": 1,
"E#O": 1,
"I#I": 2
} | mod7_arith_d2_0042 |
7 | arith | Operator definitions (evaluate strictly left to right, all results mod 7): a + b = (a + b) mod 7 a - b = (a - b) mod 7 a * b = (a × b) mod 7 a / b = (a × b⁻¹) mod 7 [b≠0].
L#P := I#N - K#J - 4. I#N := 4. K#J := 4. F#L := 6. L#P? | Operator definitions (evaluate strictly left to right, all results mod 7): a + b = (a + b) mod 7 a - b = (a - b) mod 7 a * b = (a × b) mod 7 a / b = (a × b⁻¹) mod 7 [b≠0]. | L#P := I#N - K#J - 4. I#N := 4. K#J := 4. F#L := 6. | L#P | 3 | I#N = 4 -> I#N = 4
K#J = 4 -> K#J = 4
L#P = I#N - K#J - 4
= 4 - 4 - 4
4 - 4 = (4 - 4) mod 7 = 0
0 - 4 = (0 - 4) mod 7 = 3
=> L#P = 3 | [
{
"glyph": "+",
"kind": "add",
"params": {},
"definition": "a + b = (a + b) mod 7"
},
{
"glyph": "-",
"kind": "sub",
"params": {},
"definition": "a - b = (a - b) mod 7"
},
{
"glyph": "*",
"kind": "mul",
"params": {},
"definition": "a * b = (a × b) mod 7"
},
... | 2 | 2 | 4 | 3 | 0 | {
"I#N": 1,
"F#L": 1,
"K#J": 1,
"L#P": 2
} | mod7_arith_d2_0043 |
7 | arith | Operator definitions (evaluate strictly left to right, all results mod 7): a + b = (a + b) mod 7 a - b = (a - b) mod 7 a * b = (a × b) mod 7 a / b = (a × b⁻¹) mod 7 [b≠0].
J#O := 3. G#O := 3. I#N := J#O. L#P := 6. I#N? | Operator definitions (evaluate strictly left to right, all results mod 7): a + b = (a + b) mod 7 a - b = (a - b) mod 7 a * b = (a × b) mod 7 a / b = (a × b⁻¹) mod 7 [b≠0]. | J#O := 3. G#O := 3. I#N := J#O. L#P := 6. | I#N | 3 | J#O = 3 -> J#O = 3
I#N = J#O = 3 | [
{
"glyph": "+",
"kind": "add",
"params": {},
"definition": "a + b = (a + b) mod 7"
},
{
"glyph": "-",
"kind": "sub",
"params": {},
"definition": "a - b = (a - b) mod 7"
},
{
"glyph": "*",
"kind": "mul",
"params": {},
"definition": "a * b = (a × b) mod 7"
},
... | 2 | 2 | 4 | 2 | 0 | {
"L#P": 1,
"G#O": 1,
"J#O": 1,
"I#N": 2
} | mod7_arith_d2_0044 |
7 | arith | Operator definitions (evaluate strictly left to right, all results mod 7): a + b = (a + b) mod 7 a - b = (a - b) mod 7 a * b = (a × b) mod 7 a / b = (a × b⁻¹) mod 7 [b≠0].
F#I := 3. J#N := 6. K#K := J#N. K#K? | Operator definitions (evaluate strictly left to right, all results mod 7): a + b = (a + b) mod 7 a - b = (a - b) mod 7 a * b = (a × b) mod 7 a / b = (a × b⁻¹) mod 7 [b≠0]. | F#I := 3. J#N := 6. K#K := J#N. | K#K | 6 | J#N = 6 -> J#N = 6
K#K = J#N = 6 | [
{
"glyph": "+",
"kind": "add",
"params": {},
"definition": "a + b = (a + b) mod 7"
},
{
"glyph": "-",
"kind": "sub",
"params": {},
"definition": "a - b = (a - b) mod 7"
},
{
"glyph": "*",
"kind": "mul",
"params": {},
"definition": "a * b = (a × b) mod 7"
},
... | 2 | 2 | 3 | 2 | 0 | {
"F#I": 1,
"J#N": 1,
"K#K": 2
} | mod7_arith_d2_0045 |
7 | arith | Operator definitions (evaluate strictly left to right, all results mod 7): a + b = (a + b) mod 7 a - b = (a - b) mod 7 a * b = (a × b) mod 7 a / b = (a × b⁻¹) mod 7 [b≠0].
E#I := H#P - I#P - E#N. E#N := 1. H#P := 1. I#P := 2. E#I? | Operator definitions (evaluate strictly left to right, all results mod 7): a + b = (a + b) mod 7 a - b = (a - b) mod 7 a * b = (a × b) mod 7 a / b = (a × b⁻¹) mod 7 [b≠0]. | E#I := H#P - I#P - E#N. E#N := 1. H#P := 1. I#P := 2. | E#I | 5 | H#P = 1 -> H#P = 1
E#N = 1 -> E#N = 1
I#P = 2 -> I#P = 2
E#I = H#P - I#P - E#N
= 1 - 2 - 1
1 - 2 = (1 - 2) mod 7 = 6
6 - 1 = (6 - 1) mod 7 = 5
=> E#I = 5 | [
{
"glyph": "+",
"kind": "add",
"params": {},
"definition": "a + b = (a + b) mod 7"
},
{
"glyph": "-",
"kind": "sub",
"params": {},
"definition": "a - b = (a - b) mod 7"
},
{
"glyph": "*",
"kind": "mul",
"params": {},
"definition": "a * b = (a × b) mod 7"
},
... | 2 | 2 | 4 | 4 | 0 | {
"H#P": 1,
"E#N": 1,
"I#P": 1,
"E#I": 2
} | mod7_arith_d2_0046 |
7 | arith | Operator definitions (evaluate strictly left to right, all results mod 7): a + b = (a + b) mod 7 a - b = (a - b) mod 7 a * b = (a × b) mod 7 a / b = (a × b⁻¹) mod 7 [b≠0].
H#N := 2. K#P := 4. I#J := 5. J#N := K#P - I#J. J#N? | Operator definitions (evaluate strictly left to right, all results mod 7): a + b = (a + b) mod 7 a - b = (a - b) mod 7 a * b = (a × b) mod 7 a / b = (a × b⁻¹) mod 7 [b≠0]. | H#N := 2. K#P := 4. I#J := 5. J#N := K#P - I#J. | J#N | 6 | K#P = 4 -> K#P = 4
I#J = 5 -> I#J = 5
J#N = K#P - I#J
= 4 - 5
4 - 5 = (4 - 5) mod 7 = 6
=> J#N = 6 | [
{
"glyph": "+",
"kind": "add",
"params": {},
"definition": "a + b = (a + b) mod 7"
},
{
"glyph": "-",
"kind": "sub",
"params": {},
"definition": "a - b = (a - b) mod 7"
},
{
"glyph": "*",
"kind": "mul",
"params": {},
"definition": "a * b = (a × b) mod 7"
},
... | 2 | 2 | 4 | 3 | 0 | {
"K#P": 1,
"I#J": 1,
"H#N": 1,
"J#N": 2
} | mod7_arith_d2_0047 |
7 | arith | Operator definitions (evaluate strictly left to right, all results mod 7): a + b = (a + b) mod 7 a - b = (a - b) mod 7 a * b = (a × b) mod 7 a / b = (a × b⁻¹) mod 7 [b≠0].
L#N := 6. G#I := 4. E#K := G#I - L#N. G#P := 5. G#L := 6. E#K? | Operator definitions (evaluate strictly left to right, all results mod 7): a + b = (a + b) mod 7 a - b = (a - b) mod 7 a * b = (a × b) mod 7 a / b = (a × b⁻¹) mod 7 [b≠0]. | L#N := 6. G#I := 4. E#K := G#I - L#N. G#P := 5. G#L := 6. | E#K | 5 | G#I = 4 -> G#I = 4
L#N = 6 -> L#N = 6
E#K = G#I - L#N
= 4 - 6
4 - 6 = (4 - 6) mod 7 = 5
=> E#K = 5 | [
{
"glyph": "+",
"kind": "add",
"params": {},
"definition": "a + b = (a + b) mod 7"
},
{
"glyph": "-",
"kind": "sub",
"params": {},
"definition": "a - b = (a - b) mod 7"
},
{
"glyph": "*",
"kind": "mul",
"params": {},
"definition": "a * b = (a × b) mod 7"
},
... | 2 | 2 | 5 | 3 | 0 | {
"G#I": 1,
"L#N": 1,
"G#L": 1,
"G#P": 1,
"E#K": 2
} | mod7_arith_d2_0048 |
7 | arith | Operator definitions (evaluate strictly left to right, all results mod 7): a + b = (a + b) mod 7 a - b = (a - b) mod 7 a * b = (a × b) mod 7 a / b = (a × b⁻¹) mod 7 [b≠0].
K#J := J#J + E#N. J#J := 3. E#N := 4. K#J? | Operator definitions (evaluate strictly left to right, all results mod 7): a + b = (a + b) mod 7 a - b = (a - b) mod 7 a * b = (a × b) mod 7 a / b = (a × b⁻¹) mod 7 [b≠0]. | K#J := J#J + E#N. J#J := 3. E#N := 4. | K#J | 0 | J#J = 3 -> J#J = 3
E#N = 4 -> E#N = 4
K#J = J#J + E#N
= 3 + 4
3 + 4 = (3 + 4) mod 7 = 0
=> K#J = 0 | [
{
"glyph": "+",
"kind": "add",
"params": {},
"definition": "a + b = (a + b) mod 7"
},
{
"glyph": "-",
"kind": "sub",
"params": {},
"definition": "a - b = (a - b) mod 7"
},
{
"glyph": "*",
"kind": "mul",
"params": {},
"definition": "a * b = (a × b) mod 7"
},
... | 2 | 2 | 3 | 3 | 0 | {
"J#J": 1,
"E#N": 1,
"K#J": 2
} | mod7_arith_d2_0049 |
7 | arith | Operator definitions (evaluate strictly left to right, all results mod 7): a + b = (a + b) mod 7 a - b = (a - b) mod 7 a * b = (a × b) mod 7 a / b = (a × b⁻¹) mod 7 [b≠0].
E#L := 1. K#K := 2. F#M := 3. I#P := F#M. I#P? | Operator definitions (evaluate strictly left to right, all results mod 7): a + b = (a + b) mod 7 a - b = (a - b) mod 7 a * b = (a × b) mod 7 a / b = (a × b⁻¹) mod 7 [b≠0]. | E#L := 1. K#K := 2. F#M := 3. I#P := F#M. | I#P | 3 | F#M = 3 -> F#M = 3
I#P = F#M = 3 | [
{
"glyph": "+",
"kind": "add",
"params": {},
"definition": "a + b = (a + b) mod 7"
},
{
"glyph": "-",
"kind": "sub",
"params": {},
"definition": "a - b = (a - b) mod 7"
},
{
"glyph": "*",
"kind": "mul",
"params": {},
"definition": "a * b = (a × b) mod 7"
},
... | 2 | 2 | 4 | 2 | 0 | {
"F#M": 1,
"E#L": 1,
"K#K": 1,
"I#P": 2
} | mod7_arith_d2_0050 |
7 | arith | Operator definitions (evaluate strictly left to right, all results mod 7): a + b = (a + b) mod 7 a - b = (a - b) mod 7 a * b = (a × b) mod 7 a / b = (a × b⁻¹) mod 7 [b≠0].
H#I := F#L. J#M := 6. F#L := 2. H#I? | Operator definitions (evaluate strictly left to right, all results mod 7): a + b = (a + b) mod 7 a - b = (a - b) mod 7 a * b = (a × b) mod 7 a / b = (a × b⁻¹) mod 7 [b≠0]. | H#I := F#L. J#M := 6. F#L := 2. | H#I | 2 | F#L = 2 -> F#L = 2
H#I = F#L = 2 | [
{
"glyph": "+",
"kind": "add",
"params": {},
"definition": "a + b = (a + b) mod 7"
},
{
"glyph": "-",
"kind": "sub",
"params": {},
"definition": "a - b = (a - b) mod 7"
},
{
"glyph": "*",
"kind": "mul",
"params": {},
"definition": "a * b = (a × b) mod 7"
},
... | 2 | 2 | 3 | 2 | 0 | {
"J#M": 1,
"F#L": 1,
"H#I": 2
} | mod7_arith_d2_0051 |
7 | arith | Operator definitions (evaluate strictly left to right, all results mod 7): a + b = (a + b) mod 7 a - b = (a - b) mod 7 a * b = (a × b) mod 7 a / b = (a × b⁻¹) mod 7 [b≠0].
F#K := 3. G#O := 6. H#M := 5. E#I := 2 / G#O. E#I? | Operator definitions (evaluate strictly left to right, all results mod 7): a + b = (a + b) mod 7 a - b = (a - b) mod 7 a * b = (a × b) mod 7 a / b = (a × b⁻¹) mod 7 [b≠0]. | F#K := 3. G#O := 6. H#M := 5. E#I := 2 / G#O. | E#I | 5 | G#O = 6 -> G#O = 6
E#I = 2 / G#O
= 2 / 6
2 / 6 = (2 × 6⁻¹) mod 7 = 5
=> E#I = 5 | [
{
"glyph": "+",
"kind": "add",
"params": {},
"definition": "a + b = (a + b) mod 7"
},
{
"glyph": "-",
"kind": "sub",
"params": {},
"definition": "a - b = (a - b) mod 7"
},
{
"glyph": "*",
"kind": "mul",
"params": {},
"definition": "a * b = (a × b) mod 7"
},
... | 2 | 2 | 4 | 2 | 0 | {
"F#K": 1,
"G#O": 1,
"H#M": 1,
"E#I": 2
} | mod7_arith_d2_0052 |
7 | arith | Operator definitions (evaluate strictly left to right, all results mod 7): a + b = (a + b) mod 7 a - b = (a - b) mod 7 a * b = (a × b) mod 7 a / b = (a × b⁻¹) mod 7 [b≠0].
F#K := 3. G#J := 1. G#M := 3 * F#K. I#M := 1. G#M? | Operator definitions (evaluate strictly left to right, all results mod 7): a + b = (a + b) mod 7 a - b = (a - b) mod 7 a * b = (a × b) mod 7 a / b = (a × b⁻¹) mod 7 [b≠0]. | F#K := 3. G#J := 1. G#M := 3 * F#K. I#M := 1. | G#M | 2 | F#K = 3 -> F#K = 3
G#M = 3 * F#K
= 3 * 3
3 * 3 = (3 × 3) mod 7 = 2
=> G#M = 2 | [
{
"glyph": "+",
"kind": "add",
"params": {},
"definition": "a + b = (a + b) mod 7"
},
{
"glyph": "-",
"kind": "sub",
"params": {},
"definition": "a - b = (a - b) mod 7"
},
{
"glyph": "*",
"kind": "mul",
"params": {},
"definition": "a * b = (a × b) mod 7"
},
... | 2 | 2 | 4 | 2 | 0 | {
"I#M": 1,
"G#J": 1,
"F#K": 1,
"G#M": 2
} | mod7_arith_d2_0053 |
7 | arith | Operator definitions (evaluate strictly left to right, all results mod 7): a + b = (a + b) mod 7 a - b = (a - b) mod 7 a * b = (a × b) mod 7 a / b = (a × b⁻¹) mod 7 [b≠0].
J#K := K#I. K#P := 6. K#I := 3. J#K? | Operator definitions (evaluate strictly left to right, all results mod 7): a + b = (a + b) mod 7 a - b = (a - b) mod 7 a * b = (a × b) mod 7 a / b = (a × b⁻¹) mod 7 [b≠0]. | J#K := K#I. K#P := 6. K#I := 3. | J#K | 3 | K#I = 3 -> K#I = 3
J#K = K#I = 3 | [
{
"glyph": "+",
"kind": "add",
"params": {},
"definition": "a + b = (a + b) mod 7"
},
{
"glyph": "-",
"kind": "sub",
"params": {},
"definition": "a - b = (a - b) mod 7"
},
{
"glyph": "*",
"kind": "mul",
"params": {},
"definition": "a * b = (a × b) mod 7"
},
... | 2 | 2 | 3 | 2 | 0 | {
"K#I": 1,
"K#P": 1,
"J#K": 2
} | mod7_arith_d2_0054 |
7 | arith | Operator definitions (evaluate strictly left to right, all results mod 7): a + b = (a + b) mod 7 a - b = (a - b) mod 7 a * b = (a × b) mod 7 a / b = (a × b⁻¹) mod 7 [b≠0].
K#L := 6. I#J := 1. G#L := I#J - K#L. G#L? | Operator definitions (evaluate strictly left to right, all results mod 7): a + b = (a + b) mod 7 a - b = (a - b) mod 7 a * b = (a × b) mod 7 a / b = (a × b⁻¹) mod 7 [b≠0]. | K#L := 6. I#J := 1. G#L := I#J - K#L. | G#L | 2 | K#L = 6 -> K#L = 6
I#J = 1 -> I#J = 1
G#L = I#J - K#L
= 1 - 6
1 - 6 = (1 - 6) mod 7 = 2
=> G#L = 2 | [
{
"glyph": "+",
"kind": "add",
"params": {},
"definition": "a + b = (a + b) mod 7"
},
{
"glyph": "-",
"kind": "sub",
"params": {},
"definition": "a - b = (a - b) mod 7"
},
{
"glyph": "*",
"kind": "mul",
"params": {},
"definition": "a * b = (a × b) mod 7"
},
... | 2 | 2 | 3 | 3 | 0 | {
"K#L": 1,
"I#J": 1,
"G#L": 2
} | mod7_arith_d2_0055 |
7 | arith | Operator definitions (evaluate strictly left to right, all results mod 7): a + b = (a + b) mod 7 a - b = (a - b) mod 7 a * b = (a × b) mod 7 a / b = (a × b⁻¹) mod 7 [b≠0].
I#N := J#J - J#L. J#J := 4. K#P := 1. E#J := 6. J#L := 1. I#N? | Operator definitions (evaluate strictly left to right, all results mod 7): a + b = (a + b) mod 7 a - b = (a - b) mod 7 a * b = (a × b) mod 7 a / b = (a × b⁻¹) mod 7 [b≠0]. | I#N := J#J - J#L. J#J := 4. K#P := 1. E#J := 6. J#L := 1. | I#N | 3 | J#L = 1 -> J#L = 1
J#J = 4 -> J#J = 4
I#N = J#J - J#L
= 4 - 1
4 - 1 = (4 - 1) mod 7 = 3
=> I#N = 3 | [
{
"glyph": "+",
"kind": "add",
"params": {},
"definition": "a + b = (a + b) mod 7"
},
{
"glyph": "-",
"kind": "sub",
"params": {},
"definition": "a - b = (a - b) mod 7"
},
{
"glyph": "*",
"kind": "mul",
"params": {},
"definition": "a * b = (a × b) mod 7"
},
... | 2 | 2 | 5 | 3 | 0 | {
"K#P": 1,
"J#L": 1,
"J#J": 1,
"E#J": 1,
"I#N": 2
} | mod7_arith_d2_0056 |
7 | arith | Operator definitions (evaluate strictly left to right, all results mod 7): a + b = (a + b) mod 7 a - b = (a - b) mod 7 a * b = (a × b) mod 7 a / b = (a × b⁻¹) mod 7 [b≠0].
I#O := 4. E#L := 4. E#J := 4. G#M := E#L / 4. K#N := 2. G#M? | Operator definitions (evaluate strictly left to right, all results mod 7): a + b = (a + b) mod 7 a - b = (a - b) mod 7 a * b = (a × b) mod 7 a / b = (a × b⁻¹) mod 7 [b≠0]. | I#O := 4. E#L := 4. E#J := 4. G#M := E#L / 4. K#N := 2. | G#M | 1 | E#L = 4 -> E#L = 4
G#M = E#L / 4
= 4 / 4
4 / 4 = (4 × 4⁻¹) mod 7 = 1
=> G#M = 1 | [
{
"glyph": "+",
"kind": "add",
"params": {},
"definition": "a + b = (a + b) mod 7"
},
{
"glyph": "-",
"kind": "sub",
"params": {},
"definition": "a - b = (a - b) mod 7"
},
{
"glyph": "*",
"kind": "mul",
"params": {},
"definition": "a * b = (a × b) mod 7"
},
... | 2 | 2 | 5 | 2 | 0 | {
"I#O": 1,
"E#J": 1,
"E#L": 1,
"K#N": 1,
"G#M": 2
} | mod7_arith_d2_0057 |
7 | arith | Operator definitions (evaluate strictly left to right, all results mod 7): a + b = (a + b) mod 7 a - b = (a - b) mod 7 a * b = (a × b) mod 7 a / b = (a × b⁻¹) mod 7 [b≠0].
L#O := 5. E#M := L#O - 6 - G#O. G#O := 3. J#J := 5. E#M? | Operator definitions (evaluate strictly left to right, all results mod 7): a + b = (a + b) mod 7 a - b = (a - b) mod 7 a * b = (a × b) mod 7 a / b = (a × b⁻¹) mod 7 [b≠0]. | L#O := 5. E#M := L#O - 6 - G#O. G#O := 3. J#J := 5. | E#M | 3 | G#O = 3 -> G#O = 3
L#O = 5 -> L#O = 5
E#M = L#O - 6 - G#O
= 5 - 6 - 3
5 - 6 = (5 - 6) mod 7 = 6
6 - 3 = (6 - 3) mod 7 = 3
=> E#M = 3 | [
{
"glyph": "+",
"kind": "add",
"params": {},
"definition": "a + b = (a + b) mod 7"
},
{
"glyph": "-",
"kind": "sub",
"params": {},
"definition": "a - b = (a - b) mod 7"
},
{
"glyph": "*",
"kind": "mul",
"params": {},
"definition": "a * b = (a × b) mod 7"
},
... | 2 | 2 | 4 | 3 | 0 | {
"G#O": 1,
"L#O": 1,
"J#J": 1,
"E#M": 2
} | mod7_arith_d2_0058 |
7 | arith | Operator definitions (evaluate strictly left to right, all results mod 7): a + b = (a + b) mod 7 a - b = (a - b) mod 7 a * b = (a × b) mod 7 a / b = (a × b⁻¹) mod 7 [b≠0].
H#O := 2. F#M := H#O - 2. K#K := 5. F#M? | Operator definitions (evaluate strictly left to right, all results mod 7): a + b = (a + b) mod 7 a - b = (a - b) mod 7 a * b = (a × b) mod 7 a / b = (a × b⁻¹) mod 7 [b≠0]. | H#O := 2. F#M := H#O - 2. K#K := 5. | F#M | 0 | H#O = 2 -> H#O = 2
F#M = H#O - 2
= 2 - 2
2 - 2 = (2 - 2) mod 7 = 0
=> F#M = 0 | [
{
"glyph": "+",
"kind": "add",
"params": {},
"definition": "a + b = (a + b) mod 7"
},
{
"glyph": "-",
"kind": "sub",
"params": {},
"definition": "a - b = (a - b) mod 7"
},
{
"glyph": "*",
"kind": "mul",
"params": {},
"definition": "a * b = (a × b) mod 7"
},
... | 2 | 2 | 3 | 2 | 0 | {
"K#K": 1,
"H#O": 1,
"F#M": 2
} | mod7_arith_d2_0059 |
7 | arith | Operator definitions (evaluate strictly left to right, all results mod 7): a + b = (a + b) mod 7 a - b = (a - b) mod 7 a * b = (a × b) mod 7 a / b = (a × b⁻¹) mod 7 [b≠0].
K#L := 2. H#M := K#L + I#L. I#L := 2. E#O := 5. H#M? | Operator definitions (evaluate strictly left to right, all results mod 7): a + b = (a + b) mod 7 a - b = (a - b) mod 7 a * b = (a × b) mod 7 a / b = (a × b⁻¹) mod 7 [b≠0]. | K#L := 2. H#M := K#L + I#L. I#L := 2. E#O := 5. | H#M | 4 | I#L = 2 -> I#L = 2
K#L = 2 -> K#L = 2
H#M = K#L + I#L
= 2 + 2
2 + 2 = (2 + 2) mod 7 = 4
=> H#M = 4 | [
{
"glyph": "+",
"kind": "add",
"params": {},
"definition": "a + b = (a + b) mod 7"
},
{
"glyph": "-",
"kind": "sub",
"params": {},
"definition": "a - b = (a - b) mod 7"
},
{
"glyph": "*",
"kind": "mul",
"params": {},
"definition": "a * b = (a × b) mod 7"
},
... | 2 | 2 | 4 | 3 | 0 | {
"E#O": 1,
"I#L": 1,
"K#L": 1,
"H#M": 2
} | mod7_arith_d2_0060 |
7 | arith | Operator definitions (evaluate strictly left to right, all results mod 7): a + b = (a + b) mod 7 a - b = (a - b) mod 7 a * b = (a × b) mod 7 a / b = (a × b⁻¹) mod 7 [b≠0].
E#P := 3. L#M := G#P. G#P := 1. H#N := 3. J#M := 6. L#M? | Operator definitions (evaluate strictly left to right, all results mod 7): a + b = (a + b) mod 7 a - b = (a - b) mod 7 a * b = (a × b) mod 7 a / b = (a × b⁻¹) mod 7 [b≠0]. | E#P := 3. L#M := G#P. G#P := 1. H#N := 3. J#M := 6. | L#M | 1 | G#P = 1 -> G#P = 1
L#M = G#P = 1 | [
{
"glyph": "+",
"kind": "add",
"params": {},
"definition": "a + b = (a + b) mod 7"
},
{
"glyph": "-",
"kind": "sub",
"params": {},
"definition": "a - b = (a - b) mod 7"
},
{
"glyph": "*",
"kind": "mul",
"params": {},
"definition": "a * b = (a × b) mod 7"
},
... | 2 | 2 | 5 | 2 | 0 | {
"J#M": 1,
"E#P": 1,
"G#P": 1,
"H#N": 1,
"L#M": 2
} | mod7_arith_d2_0061 |
7 | arith | Operator definitions (evaluate strictly left to right, all results mod 7): a + b = (a + b) mod 7 a - b = (a - b) mod 7 a * b = (a × b) mod 7 a / b = (a × b⁻¹) mod 7 [b≠0].
K#M := 1. K#P := 2. G#I := K#M. G#I? | Operator definitions (evaluate strictly left to right, all results mod 7): a + b = (a + b) mod 7 a - b = (a - b) mod 7 a * b = (a × b) mod 7 a / b = (a × b⁻¹) mod 7 [b≠0]. | K#M := 1. K#P := 2. G#I := K#M. | G#I | 1 | K#M = 1 -> K#M = 1
G#I = K#M = 1 | [
{
"glyph": "+",
"kind": "add",
"params": {},
"definition": "a + b = (a + b) mod 7"
},
{
"glyph": "-",
"kind": "sub",
"params": {},
"definition": "a - b = (a - b) mod 7"
},
{
"glyph": "*",
"kind": "mul",
"params": {},
"definition": "a * b = (a × b) mod 7"
},
... | 2 | 2 | 3 | 2 | 0 | {
"K#P": 1,
"K#M": 1,
"G#I": 2
} | mod7_arith_d2_0062 |
7 | arith | Operator definitions (evaluate strictly left to right, all results mod 7): a + b = (a + b) mod 7 a - b = (a - b) mod 7 a * b = (a × b) mod 7 a / b = (a × b⁻¹) mod 7 [b≠0].
L#O := 6. J#J := E#N. E#N := 2. J#J? | Operator definitions (evaluate strictly left to right, all results mod 7): a + b = (a + b) mod 7 a - b = (a - b) mod 7 a * b = (a × b) mod 7 a / b = (a × b⁻¹) mod 7 [b≠0]. | L#O := 6. J#J := E#N. E#N := 2. | J#J | 2 | E#N = 2 -> E#N = 2
J#J = E#N = 2 | [
{
"glyph": "+",
"kind": "add",
"params": {},
"definition": "a + b = (a + b) mod 7"
},
{
"glyph": "-",
"kind": "sub",
"params": {},
"definition": "a - b = (a - b) mod 7"
},
{
"glyph": "*",
"kind": "mul",
"params": {},
"definition": "a * b = (a × b) mod 7"
},
... | 2 | 2 | 3 | 2 | 0 | {
"E#N": 1,
"L#O": 1,
"J#J": 2
} | mod7_arith_d2_0063 |
7 | arith | Operator definitions (evaluate strictly left to right, all results mod 7): a + b = (a + b) mod 7 a - b = (a - b) mod 7 a * b = (a × b) mod 7 a / b = (a × b⁻¹) mod 7 [b≠0].
I#J := 4. G#O := 5 * E#K. E#I := 3. I#M := 1. E#K := 1. G#O? | Operator definitions (evaluate strictly left to right, all results mod 7): a + b = (a + b) mod 7 a - b = (a - b) mod 7 a * b = (a × b) mod 7 a / b = (a × b⁻¹) mod 7 [b≠0]. | I#J := 4. G#O := 5 * E#K. E#I := 3. I#M := 1. E#K := 1. | G#O | 5 | E#K = 1 -> E#K = 1
G#O = 5 * E#K
= 5 * 1
5 * 1 = (5 × 1) mod 7 = 5
=> G#O = 5 | [
{
"glyph": "+",
"kind": "add",
"params": {},
"definition": "a + b = (a + b) mod 7"
},
{
"glyph": "-",
"kind": "sub",
"params": {},
"definition": "a - b = (a - b) mod 7"
},
{
"glyph": "*",
"kind": "mul",
"params": {},
"definition": "a * b = (a × b) mod 7"
},
... | 2 | 2 | 5 | 2 | 0 | {
"E#K": 1,
"I#M": 1,
"E#I": 1,
"I#J": 1,
"G#O": 2
} | mod7_arith_d2_0064 |
7 | arith | Operator definitions (evaluate strictly left to right, all results mod 7): a + b = (a + b) mod 7 a - b = (a - b) mod 7 a * b = (a × b) mod 7 a / b = (a × b⁻¹) mod 7 [b≠0].
G#I := 2. H#L := 6. F#L := G#I - H#L. F#L? | Operator definitions (evaluate strictly left to right, all results mod 7): a + b = (a + b) mod 7 a - b = (a - b) mod 7 a * b = (a × b) mod 7 a / b = (a × b⁻¹) mod 7 [b≠0]. | G#I := 2. H#L := 6. F#L := G#I - H#L. | F#L | 3 | H#L = 6 -> H#L = 6
G#I = 2 -> G#I = 2
F#L = G#I - H#L
= 2 - 6
2 - 6 = (2 - 6) mod 7 = 3
=> F#L = 3 | [
{
"glyph": "+",
"kind": "add",
"params": {},
"definition": "a + b = (a + b) mod 7"
},
{
"glyph": "-",
"kind": "sub",
"params": {},
"definition": "a - b = (a - b) mod 7"
},
{
"glyph": "*",
"kind": "mul",
"params": {},
"definition": "a * b = (a × b) mod 7"
},
... | 2 | 2 | 3 | 3 | 0 | {
"H#L": 1,
"G#I": 1,
"F#L": 2
} | mod7_arith_d2_0065 |
7 | arith | Operator definitions (evaluate strictly left to right, all results mod 7): a + b = (a + b) mod 7 a - b = (a - b) mod 7 a * b = (a × b) mod 7 a / b = (a × b⁻¹) mod 7 [b≠0].
H#J := 3. E#J := 2. L#K := 2. H#O := 3. I#N := H#O - 2. I#N? | Operator definitions (evaluate strictly left to right, all results mod 7): a + b = (a + b) mod 7 a - b = (a - b) mod 7 a * b = (a × b) mod 7 a / b = (a × b⁻¹) mod 7 [b≠0]. | H#J := 3. E#J := 2. L#K := 2. H#O := 3. I#N := H#O - 2. | I#N | 1 | H#O = 3 -> H#O = 3
I#N = H#O - 2
= 3 - 2
3 - 2 = (3 - 2) mod 7 = 1
=> I#N = 1 | [
{
"glyph": "+",
"kind": "add",
"params": {},
"definition": "a + b = (a + b) mod 7"
},
{
"glyph": "-",
"kind": "sub",
"params": {},
"definition": "a - b = (a - b) mod 7"
},
{
"glyph": "*",
"kind": "mul",
"params": {},
"definition": "a * b = (a × b) mod 7"
},
... | 2 | 2 | 5 | 2 | 0 | {
"H#J": 1,
"L#K": 1,
"H#O": 1,
"E#J": 1,
"I#N": 2
} | mod7_arith_d2_0066 |
7 | arith | Operator definitions (evaluate strictly left to right, all results mod 7): a + b = (a + b) mod 7 a - b = (a - b) mod 7 a * b = (a × b) mod 7 a / b = (a × b⁻¹) mod 7 [b≠0].
F#K := 4. G#J := 4. E#K := G#L / F#K. K#J := 5. G#L := 5. E#K? | Operator definitions (evaluate strictly left to right, all results mod 7): a + b = (a + b) mod 7 a - b = (a - b) mod 7 a * b = (a × b) mod 7 a / b = (a × b⁻¹) mod 7 [b≠0]. | F#K := 4. G#J := 4. E#K := G#L / F#K. K#J := 5. G#L := 5. | E#K | 3 | G#L = 5 -> G#L = 5
F#K = 4 -> F#K = 4
E#K = G#L / F#K
= 5 / 4
5 / 4 = (5 × 4⁻¹) mod 7 = 3
=> E#K = 3 | [
{
"glyph": "+",
"kind": "add",
"params": {},
"definition": "a + b = (a + b) mod 7"
},
{
"glyph": "-",
"kind": "sub",
"params": {},
"definition": "a - b = (a - b) mod 7"
},
{
"glyph": "*",
"kind": "mul",
"params": {},
"definition": "a * b = (a × b) mod 7"
},
... | 2 | 2 | 5 | 3 | 0 | {
"K#J": 1,
"G#L": 1,
"G#J": 1,
"F#K": 1,
"E#K": 2
} | mod7_arith_d2_0067 |
7 | arith | Operator definitions (evaluate strictly left to right, all results mod 7): a + b = (a + b) mod 7 a - b = (a - b) mod 7 a * b = (a × b) mod 7 a / b = (a × b⁻¹) mod 7 [b≠0].
F#L := I#P. E#I := 1. K#K := 2. I#P := 3. F#L? | Operator definitions (evaluate strictly left to right, all results mod 7): a + b = (a + b) mod 7 a - b = (a - b) mod 7 a * b = (a × b) mod 7 a / b = (a × b⁻¹) mod 7 [b≠0]. | F#L := I#P. E#I := 1. K#K := 2. I#P := 3. | F#L | 3 | I#P = 3 -> I#P = 3
F#L = I#P = 3 | [
{
"glyph": "+",
"kind": "add",
"params": {},
"definition": "a + b = (a + b) mod 7"
},
{
"glyph": "-",
"kind": "sub",
"params": {},
"definition": "a - b = (a - b) mod 7"
},
{
"glyph": "*",
"kind": "mul",
"params": {},
"definition": "a * b = (a × b) mod 7"
},
... | 2 | 2 | 4 | 2 | 0 | {
"K#K": 1,
"I#P": 1,
"E#I": 1,
"F#L": 2
} | mod7_arith_d2_0068 |
7 | arith | Operator definitions (evaluate strictly left to right, all results mod 7): a + b = (a + b) mod 7 a - b = (a - b) mod 7 a * b = (a × b) mod 7 a / b = (a × b⁻¹) mod 7 [b≠0].
K#I := K#J - E#I. K#J := 4. E#I := 1. K#I? | Operator definitions (evaluate strictly left to right, all results mod 7): a + b = (a + b) mod 7 a - b = (a - b) mod 7 a * b = (a × b) mod 7 a / b = (a × b⁻¹) mod 7 [b≠0]. | K#I := K#J - E#I. K#J := 4. E#I := 1. | K#I | 3 | E#I = 1 -> E#I = 1
K#J = 4 -> K#J = 4
K#I = K#J - E#I
= 4 - 1
4 - 1 = (4 - 1) mod 7 = 3
=> K#I = 3 | [
{
"glyph": "+",
"kind": "add",
"params": {},
"definition": "a + b = (a + b) mod 7"
},
{
"glyph": "-",
"kind": "sub",
"params": {},
"definition": "a - b = (a - b) mod 7"
},
{
"glyph": "*",
"kind": "mul",
"params": {},
"definition": "a * b = (a × b) mod 7"
},
... | 2 | 2 | 3 | 3 | 0 | {
"E#I": 1,
"K#J": 1,
"K#I": 2
} | mod7_arith_d2_0069 |
7 | arith | Operator definitions (evaluate strictly left to right, all results mod 7): a + b = (a + b) mod 7 a - b = (a - b) mod 7 a * b = (a × b) mod 7 a / b = (a × b⁻¹) mod 7 [b≠0].
F#P := E#I. I#J := 2. E#I := 6. F#K := 6. I#L := 6. F#P? | Operator definitions (evaluate strictly left to right, all results mod 7): a + b = (a + b) mod 7 a - b = (a - b) mod 7 a * b = (a × b) mod 7 a / b = (a × b⁻¹) mod 7 [b≠0]. | F#P := E#I. I#J := 2. E#I := 6. F#K := 6. I#L := 6. | F#P | 6 | E#I = 6 -> E#I = 6
F#P = E#I = 6 | [
{
"glyph": "+",
"kind": "add",
"params": {},
"definition": "a + b = (a + b) mod 7"
},
{
"glyph": "-",
"kind": "sub",
"params": {},
"definition": "a - b = (a - b) mod 7"
},
{
"glyph": "*",
"kind": "mul",
"params": {},
"definition": "a * b = (a × b) mod 7"
},
... | 2 | 2 | 5 | 2 | 0 | {
"I#J": 1,
"I#L": 1,
"F#K": 1,
"E#I": 1,
"F#P": 2
} | mod7_arith_d2_0070 |
7 | arith | Operator definitions (evaluate strictly left to right, all results mod 7): a + b = (a + b) mod 7 a - b = (a - b) mod 7 a * b = (a × b) mod 7 a / b = (a × b⁻¹) mod 7 [b≠0].
I#P := H#J * I#J. I#J := 2. H#J := 4. I#P? | Operator definitions (evaluate strictly left to right, all results mod 7): a + b = (a + b) mod 7 a - b = (a - b) mod 7 a * b = (a × b) mod 7 a / b = (a × b⁻¹) mod 7 [b≠0]. | I#P := H#J * I#J. I#J := 2. H#J := 4. | I#P | 1 | I#J = 2 -> I#J = 2
H#J = 4 -> H#J = 4
I#P = H#J * I#J
= 4 * 2
4 * 2 = (4 × 2) mod 7 = 1
=> I#P = 1 | [
{
"glyph": "+",
"kind": "add",
"params": {},
"definition": "a + b = (a + b) mod 7"
},
{
"glyph": "-",
"kind": "sub",
"params": {},
"definition": "a - b = (a - b) mod 7"
},
{
"glyph": "*",
"kind": "mul",
"params": {},
"definition": "a * b = (a × b) mod 7"
},
... | 2 | 2 | 3 | 3 | 0 | {
"I#J": 1,
"H#J": 1,
"I#P": 2
} | mod7_arith_d2_0071 |
7 | arith | Operator definitions (evaluate strictly left to right, all results mod 7): a + b = (a + b) mod 7 a - b = (a - b) mod 7 a * b = (a × b) mod 7 a / b = (a × b⁻¹) mod 7 [b≠0].
K#P := 4 * 6 * L#J. H#L := 4. K#N := 6. L#J := 4. E#P := 1. K#P? | Operator definitions (evaluate strictly left to right, all results mod 7): a + b = (a + b) mod 7 a - b = (a - b) mod 7 a * b = (a × b) mod 7 a / b = (a × b⁻¹) mod 7 [b≠0]. | K#P := 4 * 6 * L#J. H#L := 4. K#N := 6. L#J := 4. E#P := 1. | K#P | 5 | L#J = 4 -> L#J = 4
K#P = 4 * 6 * L#J
= 4 * 6 * 4
4 * 6 = (4 × 6) mod 7 = 3
3 * 4 = (3 × 4) mod 7 = 5
=> K#P = 5 | [
{
"glyph": "+",
"kind": "add",
"params": {},
"definition": "a + b = (a + b) mod 7"
},
{
"glyph": "-",
"kind": "sub",
"params": {},
"definition": "a - b = (a - b) mod 7"
},
{
"glyph": "*",
"kind": "mul",
"params": {},
"definition": "a * b = (a × b) mod 7"
},
... | 2 | 2 | 5 | 2 | 0 | {
"H#L": 1,
"L#J": 1,
"K#N": 1,
"E#P": 1,
"K#P": 2
} | mod7_arith_d2_0072 |
7 | arith | Operator definitions (evaluate strictly left to right, all results mod 7): a + b = (a + b) mod 7 a - b = (a - b) mod 7 a * b = (a × b) mod 7 a / b = (a × b⁻¹) mod 7 [b≠0].
K#I := 6. H#I := K#I - 2. I#K := 4. G#I := 1. H#J := 1. H#I? | Operator definitions (evaluate strictly left to right, all results mod 7): a + b = (a + b) mod 7 a - b = (a - b) mod 7 a * b = (a × b) mod 7 a / b = (a × b⁻¹) mod 7 [b≠0]. | K#I := 6. H#I := K#I - 2. I#K := 4. G#I := 1. H#J := 1. | H#I | 4 | K#I = 6 -> K#I = 6
H#I = K#I - 2
= 6 - 2
6 - 2 = (6 - 2) mod 7 = 4
=> H#I = 4 | [
{
"glyph": "+",
"kind": "add",
"params": {},
"definition": "a + b = (a + b) mod 7"
},
{
"glyph": "-",
"kind": "sub",
"params": {},
"definition": "a - b = (a - b) mod 7"
},
{
"glyph": "*",
"kind": "mul",
"params": {},
"definition": "a * b = (a × b) mod 7"
},
... | 2 | 2 | 5 | 2 | 0 | {
"H#J": 1,
"I#K": 1,
"K#I": 1,
"G#I": 1,
"H#I": 2
} | mod7_arith_d2_0073 |
7 | arith | Operator definitions (evaluate strictly left to right, all results mod 7): a + b = (a + b) mod 7 a - b = (a - b) mod 7 a * b = (a × b) mod 7 a / b = (a × b⁻¹) mod 7 [b≠0].
L#P := H#L. H#L := 6. H#M := 1. L#P? | Operator definitions (evaluate strictly left to right, all results mod 7): a + b = (a + b) mod 7 a - b = (a - b) mod 7 a * b = (a × b) mod 7 a / b = (a × b⁻¹) mod 7 [b≠0]. | L#P := H#L. H#L := 6. H#M := 1. | L#P | 6 | H#L = 6 -> H#L = 6
L#P = H#L = 6 | [
{
"glyph": "+",
"kind": "add",
"params": {},
"definition": "a + b = (a + b) mod 7"
},
{
"glyph": "-",
"kind": "sub",
"params": {},
"definition": "a - b = (a - b) mod 7"
},
{
"glyph": "*",
"kind": "mul",
"params": {},
"definition": "a * b = (a × b) mod 7"
},
... | 2 | 2 | 3 | 2 | 0 | {
"H#M": 1,
"H#L": 1,
"L#P": 2
} | mod7_arith_d2_0074 |
7 | arith | Operator definitions (evaluate strictly left to right, all results mod 7): a + b = (a + b) mod 7 a - b = (a - b) mod 7 a * b = (a × b) mod 7 a / b = (a × b⁻¹) mod 7 [b≠0].
G#K := 3. H#O := 1. L#P := 5. G#J := H#O * G#K. G#J? | Operator definitions (evaluate strictly left to right, all results mod 7): a + b = (a + b) mod 7 a - b = (a - b) mod 7 a * b = (a × b) mod 7 a / b = (a × b⁻¹) mod 7 [b≠0]. | G#K := 3. H#O := 1. L#P := 5. G#J := H#O * G#K. | G#J | 3 | H#O = 1 -> H#O = 1
G#K = 3 -> G#K = 3
G#J = H#O * G#K
= 1 * 3
1 * 3 = (1 × 3) mod 7 = 3
=> G#J = 3 | [
{
"glyph": "+",
"kind": "add",
"params": {},
"definition": "a + b = (a + b) mod 7"
},
{
"glyph": "-",
"kind": "sub",
"params": {},
"definition": "a - b = (a - b) mod 7"
},
{
"glyph": "*",
"kind": "mul",
"params": {},
"definition": "a * b = (a × b) mod 7"
},
... | 2 | 2 | 4 | 3 | 0 | {
"H#O": 1,
"L#P": 1,
"G#K": 1,
"G#J": 2
} | mod7_arith_d2_0075 |
7 | arith | Operator definitions (evaluate strictly left to right, all results mod 7): a + b = (a + b) mod 7 a - b = (a - b) mod 7 a * b = (a × b) mod 7 a / b = (a × b⁻¹) mod 7 [b≠0].
J#N := 1. H#K := 5. H#I := H#K / J#N. H#I? | Operator definitions (evaluate strictly left to right, all results mod 7): a + b = (a + b) mod 7 a - b = (a - b) mod 7 a * b = (a × b) mod 7 a / b = (a × b⁻¹) mod 7 [b≠0]. | J#N := 1. H#K := 5. H#I := H#K / J#N. | H#I | 5 | H#K = 5 -> H#K = 5
J#N = 1 -> J#N = 1
H#I = H#K / J#N
= 5 / 1
5 / 1 = (5 × 1⁻¹) mod 7 = 5
=> H#I = 5 | [
{
"glyph": "+",
"kind": "add",
"params": {},
"definition": "a + b = (a + b) mod 7"
},
{
"glyph": "-",
"kind": "sub",
"params": {},
"definition": "a - b = (a - b) mod 7"
},
{
"glyph": "*",
"kind": "mul",
"params": {},
"definition": "a * b = (a × b) mod 7"
},
... | 2 | 2 | 3 | 3 | 0 | {
"H#K": 1,
"J#N": 1,
"H#I": 2
} | mod7_arith_d2_0076 |
7 | arith | Operator definitions (evaluate strictly left to right, all results mod 7): a + b = (a + b) mod 7 a - b = (a - b) mod 7 a * b = (a × b) mod 7 a / b = (a × b⁻¹) mod 7 [b≠0].
E#O := 1. H#J := 3. J#K := 5. I#P := I#N + J#K. I#N := 4. I#P? | Operator definitions (evaluate strictly left to right, all results mod 7): a + b = (a + b) mod 7 a - b = (a - b) mod 7 a * b = (a × b) mod 7 a / b = (a × b⁻¹) mod 7 [b≠0]. | E#O := 1. H#J := 3. J#K := 5. I#P := I#N + J#K. I#N := 4. | I#P | 2 | J#K = 5 -> J#K = 5
I#N = 4 -> I#N = 4
I#P = I#N + J#K
= 4 + 5
4 + 5 = (4 + 5) mod 7 = 2
=> I#P = 2 | [
{
"glyph": "+",
"kind": "add",
"params": {},
"definition": "a + b = (a + b) mod 7"
},
{
"glyph": "-",
"kind": "sub",
"params": {},
"definition": "a - b = (a - b) mod 7"
},
{
"glyph": "*",
"kind": "mul",
"params": {},
"definition": "a * b = (a × b) mod 7"
},
... | 2 | 2 | 5 | 3 | 0 | {
"E#O": 1,
"J#K": 1,
"H#J": 1,
"I#N": 1,
"I#P": 2
} | mod7_arith_d2_0077 |
7 | arith | Operator definitions (evaluate strictly left to right, all results mod 7): a + b = (a + b) mod 7 a - b = (a - b) mod 7 a * b = (a × b) mod 7 a / b = (a × b⁻¹) mod 7 [b≠0].
H#J := 5. I#O := 1. J#M := G#N. I#I := 1. G#N := 2. J#M? | Operator definitions (evaluate strictly left to right, all results mod 7): a + b = (a + b) mod 7 a - b = (a - b) mod 7 a * b = (a × b) mod 7 a / b = (a × b⁻¹) mod 7 [b≠0]. | H#J := 5. I#O := 1. J#M := G#N. I#I := 1. G#N := 2. | J#M | 2 | G#N = 2 -> G#N = 2
J#M = G#N = 2 | [
{
"glyph": "+",
"kind": "add",
"params": {},
"definition": "a + b = (a + b) mod 7"
},
{
"glyph": "-",
"kind": "sub",
"params": {},
"definition": "a - b = (a - b) mod 7"
},
{
"glyph": "*",
"kind": "mul",
"params": {},
"definition": "a * b = (a × b) mod 7"
},
... | 2 | 2 | 5 | 2 | 0 | {
"I#O": 1,
"I#I": 1,
"G#N": 1,
"H#J": 1,
"J#M": 2
} | mod7_arith_d2_0078 |
7 | arith | Operator definitions (evaluate strictly left to right, all results mod 7): a + b = (a + b) mod 7 a - b = (a - b) mod 7 a * b = (a × b) mod 7 a / b = (a × b⁻¹) mod 7 [b≠0].
K#J := I#M. J#P := 4. I#M := 5. I#P := 5. K#J? | Operator definitions (evaluate strictly left to right, all results mod 7): a + b = (a + b) mod 7 a - b = (a - b) mod 7 a * b = (a × b) mod 7 a / b = (a × b⁻¹) mod 7 [b≠0]. | K#J := I#M. J#P := 4. I#M := 5. I#P := 5. | K#J | 5 | I#M = 5 -> I#M = 5
K#J = I#M = 5 | [
{
"glyph": "+",
"kind": "add",
"params": {},
"definition": "a + b = (a + b) mod 7"
},
{
"glyph": "-",
"kind": "sub",
"params": {},
"definition": "a - b = (a - b) mod 7"
},
{
"glyph": "*",
"kind": "mul",
"params": {},
"definition": "a * b = (a × b) mod 7"
},
... | 2 | 2 | 4 | 2 | 0 | {
"I#P": 1,
"I#M": 1,
"J#P": 1,
"K#J": 2
} | mod7_arith_d2_0079 |
7 | arith | Operator definitions (evaluate strictly left to right, all results mod 7): a + b = (a + b) mod 7 a - b = (a - b) mod 7 a * b = (a × b) mod 7 a / b = (a × b⁻¹) mod 7 [b≠0].
J#O := E#P + F#O. L#M := 4. F#O := 4. E#P := 5. J#O? | Operator definitions (evaluate strictly left to right, all results mod 7): a + b = (a + b) mod 7 a - b = (a - b) mod 7 a * b = (a × b) mod 7 a / b = (a × b⁻¹) mod 7 [b≠0]. | J#O := E#P + F#O. L#M := 4. F#O := 4. E#P := 5. | J#O | 2 | F#O = 4 -> F#O = 4
E#P = 5 -> E#P = 5
J#O = E#P + F#O
= 5 + 4
5 + 4 = (5 + 4) mod 7 = 2
=> J#O = 2 | [
{
"glyph": "+",
"kind": "add",
"params": {},
"definition": "a + b = (a + b) mod 7"
},
{
"glyph": "-",
"kind": "sub",
"params": {},
"definition": "a - b = (a - b) mod 7"
},
{
"glyph": "*",
"kind": "mul",
"params": {},
"definition": "a * b = (a × b) mod 7"
},
... | 2 | 2 | 4 | 3 | 0 | {
"F#O": 1,
"L#M": 1,
"E#P": 1,
"J#O": 2
} | mod7_arith_d2_0080 |
7 | arith | Operator definitions (evaluate strictly left to right, all results mod 7): a + b = (a + b) mod 7 a - b = (a - b) mod 7 a * b = (a × b) mod 7 a / b = (a × b⁻¹) mod 7 [b≠0].
E#M := K#M - K#L. K#L := 6. K#M := 5. K#O := 3. E#M? | Operator definitions (evaluate strictly left to right, all results mod 7): a + b = (a + b) mod 7 a - b = (a - b) mod 7 a * b = (a × b) mod 7 a / b = (a × b⁻¹) mod 7 [b≠0]. | E#M := K#M - K#L. K#L := 6. K#M := 5. K#O := 3. | E#M | 6 | K#L = 6 -> K#L = 6
K#M = 5 -> K#M = 5
E#M = K#M - K#L
= 5 - 6
5 - 6 = (5 - 6) mod 7 = 6
=> E#M = 6 | [
{
"glyph": "+",
"kind": "add",
"params": {},
"definition": "a + b = (a + b) mod 7"
},
{
"glyph": "-",
"kind": "sub",
"params": {},
"definition": "a - b = (a - b) mod 7"
},
{
"glyph": "*",
"kind": "mul",
"params": {},
"definition": "a * b = (a × b) mod 7"
},
... | 2 | 2 | 4 | 3 | 0 | {
"K#L": 1,
"K#M": 1,
"K#O": 1,
"E#M": 2
} | mod7_arith_d2_0081 |
7 | arith | Operator definitions (evaluate strictly left to right, all results mod 7): a + b = (a + b) mod 7 a - b = (a - b) mod 7 a * b = (a × b) mod 7 a / b = (a × b⁻¹) mod 7 [b≠0].
G#I := 1. J#O := 5. G#M := J#O / G#I / 4. F#L := 4. F#O := 3. G#M? | Operator definitions (evaluate strictly left to right, all results mod 7): a + b = (a + b) mod 7 a - b = (a - b) mod 7 a * b = (a × b) mod 7 a / b = (a × b⁻¹) mod 7 [b≠0]. | G#I := 1. J#O := 5. G#M := J#O / G#I / 4. F#L := 4. F#O := 3. | G#M | 3 | J#O = 5 -> J#O = 5
G#I = 1 -> G#I = 1
G#M = J#O / G#I / 4
= 5 / 1 / 4
5 / 1 = (5 × 1⁻¹) mod 7 = 5
5 / 4 = (5 × 4⁻¹) mod 7 = 3
=> G#M = 3 | [
{
"glyph": "+",
"kind": "add",
"params": {},
"definition": "a + b = (a + b) mod 7"
},
{
"glyph": "-",
"kind": "sub",
"params": {},
"definition": "a - b = (a - b) mod 7"
},
{
"glyph": "*",
"kind": "mul",
"params": {},
"definition": "a * b = (a × b) mod 7"
},
... | 2 | 2 | 5 | 3 | 0 | {
"J#O": 1,
"G#I": 1,
"F#L": 1,
"F#O": 1,
"G#M": 2
} | mod7_arith_d2_0082 |
7 | arith | Operator definitions (evaluate strictly left to right, all results mod 7): a + b = (a + b) mod 7 a - b = (a - b) mod 7 a * b = (a × b) mod 7 a / b = (a × b⁻¹) mod 7 [b≠0].
L#M := 2. L#O := 1. I#M := L#M + L#L. L#L := 6. I#M? | Operator definitions (evaluate strictly left to right, all results mod 7): a + b = (a + b) mod 7 a - b = (a - b) mod 7 a * b = (a × b) mod 7 a / b = (a × b⁻¹) mod 7 [b≠0]. | L#M := 2. L#O := 1. I#M := L#M + L#L. L#L := 6. | I#M | 1 | L#L = 6 -> L#L = 6
L#M = 2 -> L#M = 2
I#M = L#M + L#L
= 2 + 6
2 + 6 = (2 + 6) mod 7 = 1
=> I#M = 1 | [
{
"glyph": "+",
"kind": "add",
"params": {},
"definition": "a + b = (a + b) mod 7"
},
{
"glyph": "-",
"kind": "sub",
"params": {},
"definition": "a - b = (a - b) mod 7"
},
{
"glyph": "*",
"kind": "mul",
"params": {},
"definition": "a * b = (a × b) mod 7"
},
... | 2 | 2 | 4 | 3 | 0 | {
"L#L": 1,
"L#M": 1,
"L#O": 1,
"I#M": 2
} | mod7_arith_d2_0083 |
7 | arith | Operator definitions (evaluate strictly left to right, all results mod 7): a + b = (a + b) mod 7 a - b = (a - b) mod 7 a * b = (a × b) mod 7 a / b = (a × b⁻¹) mod 7 [b≠0].
F#J := J#M - H#L. H#L := 6. J#M := 5. F#J? | Operator definitions (evaluate strictly left to right, all results mod 7): a + b = (a + b) mod 7 a - b = (a - b) mod 7 a * b = (a × b) mod 7 a / b = (a × b⁻¹) mod 7 [b≠0]. | F#J := J#M - H#L. H#L := 6. J#M := 5. | F#J | 6 | J#M = 5 -> J#M = 5
H#L = 6 -> H#L = 6
F#J = J#M - H#L
= 5 - 6
5 - 6 = (5 - 6) mod 7 = 6
=> F#J = 6 | [
{
"glyph": "+",
"kind": "add",
"params": {},
"definition": "a + b = (a + b) mod 7"
},
{
"glyph": "-",
"kind": "sub",
"params": {},
"definition": "a - b = (a - b) mod 7"
},
{
"glyph": "*",
"kind": "mul",
"params": {},
"definition": "a * b = (a × b) mod 7"
},
... | 2 | 2 | 3 | 3 | 0 | {
"J#M": 1,
"H#L": 1,
"F#J": 2
} | mod7_arith_d2_0084 |
7 | arith | Operator definitions (evaluate strictly left to right, all results mod 7): a + b = (a + b) mod 7 a - b = (a - b) mod 7 a * b = (a × b) mod 7 a / b = (a × b⁻¹) mod 7 [b≠0].
L#P := 4. K#K := 2. E#O := 5. J#M := 2. J#O := L#P - E#O * J#M. J#O? | Operator definitions (evaluate strictly left to right, all results mod 7): a + b = (a + b) mod 7 a - b = (a - b) mod 7 a * b = (a × b) mod 7 a / b = (a × b⁻¹) mod 7 [b≠0]. | L#P := 4. K#K := 2. E#O := 5. J#M := 2. J#O := L#P - E#O * J#M. | J#O | 5 | L#P = 4 -> L#P = 4
J#M = 2 -> J#M = 2
E#O = 5 -> E#O = 5
J#O = L#P - E#O * J#M
= 4 - 5 * 2
4 - 5 = (4 - 5) mod 7 = 6
6 * 2 = (6 × 2) mod 7 = 5
=> J#O = 5 | [
{
"glyph": "+",
"kind": "add",
"params": {},
"definition": "a + b = (a + b) mod 7"
},
{
"glyph": "-",
"kind": "sub",
"params": {},
"definition": "a - b = (a - b) mod 7"
},
{
"glyph": "*",
"kind": "mul",
"params": {},
"definition": "a * b = (a × b) mod 7"
},
... | 2 | 2 | 5 | 4 | 0 | {
"L#P": 1,
"J#M": 1,
"E#O": 1,
"K#K": 1,
"J#O": 2
} | mod7_arith_d2_0085 |
7 | arith | Operator definitions (evaluate strictly left to right, all results mod 7): a + b = (a + b) mod 7 a - b = (a - b) mod 7 a * b = (a × b) mod 7 a / b = (a × b⁻¹) mod 7 [b≠0].
H#J := 1. G#M := 5. H#M := 6. L#I := H#J - H#M. L#I? | Operator definitions (evaluate strictly left to right, all results mod 7): a + b = (a + b) mod 7 a - b = (a - b) mod 7 a * b = (a × b) mod 7 a / b = (a × b⁻¹) mod 7 [b≠0]. | H#J := 1. G#M := 5. H#M := 6. L#I := H#J - H#M. | L#I | 2 | H#M = 6 -> H#M = 6
H#J = 1 -> H#J = 1
L#I = H#J - H#M
= 1 - 6
1 - 6 = (1 - 6) mod 7 = 2
=> L#I = 2 | [
{
"glyph": "+",
"kind": "add",
"params": {},
"definition": "a + b = (a + b) mod 7"
},
{
"glyph": "-",
"kind": "sub",
"params": {},
"definition": "a - b = (a - b) mod 7"
},
{
"glyph": "*",
"kind": "mul",
"params": {},
"definition": "a * b = (a × b) mod 7"
},
... | 2 | 2 | 4 | 3 | 0 | {
"H#M": 1,
"G#M": 1,
"H#J": 1,
"L#I": 2
} | mod7_arith_d2_0086 |
7 | arith | Operator definitions (evaluate strictly left to right, all results mod 7): a + b = (a + b) mod 7 a - b = (a - b) mod 7 a * b = (a × b) mod 7 a / b = (a × b⁻¹) mod 7 [b≠0].
H#J := E#P + K#K. K#K := 2. E#P := 1. J#K := 5. H#J? | Operator definitions (evaluate strictly left to right, all results mod 7): a + b = (a + b) mod 7 a - b = (a - b) mod 7 a * b = (a × b) mod 7 a / b = (a × b⁻¹) mod 7 [b≠0]. | H#J := E#P + K#K. K#K := 2. E#P := 1. J#K := 5. | H#J | 3 | E#P = 1 -> E#P = 1
K#K = 2 -> K#K = 2
H#J = E#P + K#K
= 1 + 2
1 + 2 = (1 + 2) mod 7 = 3
=> H#J = 3 | [
{
"glyph": "+",
"kind": "add",
"params": {},
"definition": "a + b = (a + b) mod 7"
},
{
"glyph": "-",
"kind": "sub",
"params": {},
"definition": "a - b = (a - b) mod 7"
},
{
"glyph": "*",
"kind": "mul",
"params": {},
"definition": "a * b = (a × b) mod 7"
},
... | 2 | 2 | 4 | 3 | 0 | {
"J#K": 1,
"E#P": 1,
"K#K": 1,
"H#J": 2
} | mod7_arith_d2_0087 |
7 | arith | Operator definitions (evaluate strictly left to right, all results mod 7): a + b = (a + b) mod 7 a - b = (a - b) mod 7 a * b = (a × b) mod 7 a / b = (a × b⁻¹) mod 7 [b≠0].
K#L := 4. H#P := F#L. F#L := 6. H#P? | Operator definitions (evaluate strictly left to right, all results mod 7): a + b = (a + b) mod 7 a - b = (a - b) mod 7 a * b = (a × b) mod 7 a / b = (a × b⁻¹) mod 7 [b≠0]. | K#L := 4. H#P := F#L. F#L := 6. | H#P | 6 | F#L = 6 -> F#L = 6
H#P = F#L = 6 | [
{
"glyph": "+",
"kind": "add",
"params": {},
"definition": "a + b = (a + b) mod 7"
},
{
"glyph": "-",
"kind": "sub",
"params": {},
"definition": "a - b = (a - b) mod 7"
},
{
"glyph": "*",
"kind": "mul",
"params": {},
"definition": "a * b = (a × b) mod 7"
},
... | 2 | 2 | 3 | 2 | 0 | {
"F#L": 1,
"K#L": 1,
"H#P": 2
} | mod7_arith_d2_0088 |
7 | arith | Operator definitions (evaluate strictly left to right, all results mod 7): a + b = (a + b) mod 7 a - b = (a - b) mod 7 a * b = (a × b) mod 7 a / b = (a × b⁻¹) mod 7 [b≠0].
H#L := 3. G#P := 6. I#J := G#P - H#L. L#N := 3. I#J? | Operator definitions (evaluate strictly left to right, all results mod 7): a + b = (a + b) mod 7 a - b = (a - b) mod 7 a * b = (a × b) mod 7 a / b = (a × b⁻¹) mod 7 [b≠0]. | H#L := 3. G#P := 6. I#J := G#P - H#L. L#N := 3. | I#J | 3 | H#L = 3 -> H#L = 3
G#P = 6 -> G#P = 6
I#J = G#P - H#L
= 6 - 3
6 - 3 = (6 - 3) mod 7 = 3
=> I#J = 3 | [
{
"glyph": "+",
"kind": "add",
"params": {},
"definition": "a + b = (a + b) mod 7"
},
{
"glyph": "-",
"kind": "sub",
"params": {},
"definition": "a - b = (a - b) mod 7"
},
{
"glyph": "*",
"kind": "mul",
"params": {},
"definition": "a * b = (a × b) mod 7"
},
... | 2 | 2 | 4 | 3 | 0 | {
"H#L": 1,
"L#N": 1,
"G#P": 1,
"I#J": 2
} | mod7_arith_d2_0089 |
7 | arith | Operator definitions (evaluate strictly left to right, all results mod 7): a + b = (a + b) mod 7 a - b = (a - b) mod 7 a * b = (a × b) mod 7 a / b = (a × b⁻¹) mod 7 [b≠0].
G#M := 6. L#K := 3. E#O := 5. J#J := G#M + E#O + L#K. J#J? | Operator definitions (evaluate strictly left to right, all results mod 7): a + b = (a + b) mod 7 a - b = (a - b) mod 7 a * b = (a × b) mod 7 a / b = (a × b⁻¹) mod 7 [b≠0]. | G#M := 6. L#K := 3. E#O := 5. J#J := G#M + E#O + L#K. | J#J | 0 | G#M = 6 -> G#M = 6
E#O = 5 -> E#O = 5
L#K = 3 -> L#K = 3
J#J = G#M + E#O + L#K
= 6 + 5 + 3
6 + 5 = (6 + 5) mod 7 = 4
4 + 3 = (4 + 3) mod 7 = 0
=> J#J = 0 | [
{
"glyph": "+",
"kind": "add",
"params": {},
"definition": "a + b = (a + b) mod 7"
},
{
"glyph": "-",
"kind": "sub",
"params": {},
"definition": "a - b = (a - b) mod 7"
},
{
"glyph": "*",
"kind": "mul",
"params": {},
"definition": "a * b = (a × b) mod 7"
},
... | 2 | 2 | 4 | 4 | 0 | {
"G#M": 1,
"E#O": 1,
"L#K": 1,
"J#J": 2
} | mod7_arith_d2_0090 |
7 | arith | Operator definitions (evaluate strictly left to right, all results mod 7): a + b = (a + b) mod 7 a - b = (a - b) mod 7 a * b = (a × b) mod 7 a / b = (a × b⁻¹) mod 7 [b≠0].
G#K := L#O / J#O. J#O := 3. J#M := 5. L#O := 4. E#K := 2. G#K? | Operator definitions (evaluate strictly left to right, all results mod 7): a + b = (a + b) mod 7 a - b = (a - b) mod 7 a * b = (a × b) mod 7 a / b = (a × b⁻¹) mod 7 [b≠0]. | G#K := L#O / J#O. J#O := 3. J#M := 5. L#O := 4. E#K := 2. | G#K | 6 | J#O = 3 -> J#O = 3
L#O = 4 -> L#O = 4
G#K = L#O / J#O
= 4 / 3
4 / 3 = (4 × 3⁻¹) mod 7 = 6
=> G#K = 6 | [
{
"glyph": "+",
"kind": "add",
"params": {},
"definition": "a + b = (a + b) mod 7"
},
{
"glyph": "-",
"kind": "sub",
"params": {},
"definition": "a - b = (a - b) mod 7"
},
{
"glyph": "*",
"kind": "mul",
"params": {},
"definition": "a * b = (a × b) mod 7"
},
... | 2 | 2 | 5 | 3 | 0 | {
"E#K": 1,
"J#O": 1,
"J#M": 1,
"L#O": 1,
"G#K": 2
} | mod7_arith_d2_0091 |
7 | arith | Operator definitions (evaluate strictly left to right, all results mod 7): a + b = (a + b) mod 7 a - b = (a - b) mod 7 a * b = (a × b) mod 7 a / b = (a × b⁻¹) mod 7 [b≠0].
E#I := 4. K#K := 2 - J#O. J#O := 2. K#K? | Operator definitions (evaluate strictly left to right, all results mod 7): a + b = (a + b) mod 7 a - b = (a - b) mod 7 a * b = (a × b) mod 7 a / b = (a × b⁻¹) mod 7 [b≠0]. | E#I := 4. K#K := 2 - J#O. J#O := 2. | K#K | 0 | J#O = 2 -> J#O = 2
K#K = 2 - J#O
= 2 - 2
2 - 2 = (2 - 2) mod 7 = 0
=> K#K = 0 | [
{
"glyph": "+",
"kind": "add",
"params": {},
"definition": "a + b = (a + b) mod 7"
},
{
"glyph": "-",
"kind": "sub",
"params": {},
"definition": "a - b = (a - b) mod 7"
},
{
"glyph": "*",
"kind": "mul",
"params": {},
"definition": "a * b = (a × b) mod 7"
},
... | 2 | 2 | 3 | 2 | 0 | {
"J#O": 1,
"E#I": 1,
"K#K": 2
} | mod7_arith_d2_0092 |
7 | arith | Operator definitions (evaluate strictly left to right, all results mod 7): a + b = (a + b) mod 7 a - b = (a - b) mod 7 a * b = (a × b) mod 7 a / b = (a × b⁻¹) mod 7 [b≠0].
G#L := H#J - E#K + E#L. E#M := 2. E#L := 3. H#J := 3. E#K := 3. G#L? | Operator definitions (evaluate strictly left to right, all results mod 7): a + b = (a + b) mod 7 a - b = (a - b) mod 7 a * b = (a × b) mod 7 a / b = (a × b⁻¹) mod 7 [b≠0]. | G#L := H#J - E#K + E#L. E#M := 2. E#L := 3. H#J := 3. E#K := 3. | G#L | 3 | H#J = 3 -> H#J = 3
E#L = 3 -> E#L = 3
E#K = 3 -> E#K = 3
G#L = H#J - E#K + E#L
= 3 - 3 + 3
3 - 3 = (3 - 3) mod 7 = 0
0 + 3 = (0 + 3) mod 7 = 3
=> G#L = 3 | [
{
"glyph": "+",
"kind": "add",
"params": {},
"definition": "a + b = (a + b) mod 7"
},
{
"glyph": "-",
"kind": "sub",
"params": {},
"definition": "a - b = (a - b) mod 7"
},
{
"glyph": "*",
"kind": "mul",
"params": {},
"definition": "a * b = (a × b) mod 7"
},
... | 2 | 2 | 5 | 4 | 0 | {
"H#J": 1,
"E#L": 1,
"E#K": 1,
"E#M": 1,
"G#L": 2
} | mod7_arith_d2_0093 |
7 | arith | Operator definitions (evaluate strictly left to right, all results mod 7): a + b = (a + b) mod 7 a - b = (a - b) mod 7 a * b = (a × b) mod 7 a / b = (a × b⁻¹) mod 7 [b≠0].
F#L := 4. J#P := 1. H#K := F#L * H#P - 4. H#P := 1. H#K? | Operator definitions (evaluate strictly left to right, all results mod 7): a + b = (a + b) mod 7 a - b = (a - b) mod 7 a * b = (a × b) mod 7 a / b = (a × b⁻¹) mod 7 [b≠0]. | F#L := 4. J#P := 1. H#K := F#L * H#P - 4. H#P := 1. | H#K | 0 | F#L = 4 -> F#L = 4
H#P = 1 -> H#P = 1
H#K = F#L * H#P - 4
= 4 * 1 - 4
4 * 1 = (4 × 1) mod 7 = 4
4 - 4 = (4 - 4) mod 7 = 0
=> H#K = 0 | [
{
"glyph": "+",
"kind": "add",
"params": {},
"definition": "a + b = (a + b) mod 7"
},
{
"glyph": "-",
"kind": "sub",
"params": {},
"definition": "a - b = (a - b) mod 7"
},
{
"glyph": "*",
"kind": "mul",
"params": {},
"definition": "a * b = (a × b) mod 7"
},
... | 2 | 2 | 4 | 3 | 0 | {
"F#L": 1,
"J#P": 1,
"H#P": 1,
"H#K": 2
} | mod7_arith_d2_0094 |
7 | arith | Operator definitions (evaluate strictly left to right, all results mod 7): a + b = (a + b) mod 7 a - b = (a - b) mod 7 a * b = (a × b) mod 7 a / b = (a × b⁻¹) mod 7 [b≠0].
H#K := F#J + K#J. F#J := 1. E#M := 1. K#J := 3. H#K? | Operator definitions (evaluate strictly left to right, all results mod 7): a + b = (a + b) mod 7 a - b = (a - b) mod 7 a * b = (a × b) mod 7 a / b = (a × b⁻¹) mod 7 [b≠0]. | H#K := F#J + K#J. F#J := 1. E#M := 1. K#J := 3. | H#K | 4 | F#J = 1 -> F#J = 1
K#J = 3 -> K#J = 3
H#K = F#J + K#J
= 1 + 3
1 + 3 = (1 + 3) mod 7 = 4
=> H#K = 4 | [
{
"glyph": "+",
"kind": "add",
"params": {},
"definition": "a + b = (a + b) mod 7"
},
{
"glyph": "-",
"kind": "sub",
"params": {},
"definition": "a - b = (a - b) mod 7"
},
{
"glyph": "*",
"kind": "mul",
"params": {},
"definition": "a * b = (a × b) mod 7"
},
... | 2 | 2 | 4 | 3 | 0 | {
"F#J": 1,
"K#J": 1,
"E#M": 1,
"H#K": 2
} | mod7_arith_d2_0095 |
7 | arith | Operator definitions (evaluate strictly left to right, all results mod 7): a + b = (a + b) mod 7 a - b = (a - b) mod 7 a * b = (a × b) mod 7 a / b = (a × b⁻¹) mod 7 [b≠0].
F#M := I#K * 6 * E#O. E#O := 3. I#K := 6. F#M? | Operator definitions (evaluate strictly left to right, all results mod 7): a + b = (a + b) mod 7 a - b = (a - b) mod 7 a * b = (a × b) mod 7 a / b = (a × b⁻¹) mod 7 [b≠0]. | F#M := I#K * 6 * E#O. E#O := 3. I#K := 6. | F#M | 3 | I#K = 6 -> I#K = 6
E#O = 3 -> E#O = 3
F#M = I#K * 6 * E#O
= 6 * 6 * 3
6 * 6 = (6 × 6) mod 7 = 1
1 * 3 = (1 × 3) mod 7 = 3
=> F#M = 3 | [
{
"glyph": "+",
"kind": "add",
"params": {},
"definition": "a + b = (a + b) mod 7"
},
{
"glyph": "-",
"kind": "sub",
"params": {},
"definition": "a - b = (a - b) mod 7"
},
{
"glyph": "*",
"kind": "mul",
"params": {},
"definition": "a * b = (a × b) mod 7"
},
... | 2 | 2 | 3 | 3 | 0 | {
"I#K": 1,
"E#O": 1,
"F#M": 2
} | mod7_arith_d2_0096 |
7 | arith | Operator definitions (evaluate strictly left to right, all results mod 7): a + b = (a + b) mod 7 a - b = (a - b) mod 7 a * b = (a × b) mod 7 a / b = (a × b⁻¹) mod 7 [b≠0].
F#M := 3. E#K := J#P + H#J. J#P := 5. H#J := 1. E#K? | Operator definitions (evaluate strictly left to right, all results mod 7): a + b = (a + b) mod 7 a - b = (a - b) mod 7 a * b = (a × b) mod 7 a / b = (a × b⁻¹) mod 7 [b≠0]. | F#M := 3. E#K := J#P + H#J. J#P := 5. H#J := 1. | E#K | 6 | H#J = 1 -> H#J = 1
J#P = 5 -> J#P = 5
E#K = J#P + H#J
= 5 + 1
5 + 1 = (5 + 1) mod 7 = 6
=> E#K = 6 | [
{
"glyph": "+",
"kind": "add",
"params": {},
"definition": "a + b = (a + b) mod 7"
},
{
"glyph": "-",
"kind": "sub",
"params": {},
"definition": "a - b = (a - b) mod 7"
},
{
"glyph": "*",
"kind": "mul",
"params": {},
"definition": "a * b = (a × b) mod 7"
},
... | 2 | 2 | 4 | 3 | 0 | {
"F#M": 1,
"H#J": 1,
"J#P": 1,
"E#K": 2
} | mod7_arith_d2_0097 |
7 | arith | Operator definitions (evaluate strictly left to right, all results mod 7): a + b = (a + b) mod 7 a - b = (a - b) mod 7 a * b = (a × b) mod 7 a / b = (a × b⁻¹) mod 7 [b≠0].
F#N := K#O / I#K. I#K := 6. K#O := 6. G#M := 3. E#O := 2. F#N? | Operator definitions (evaluate strictly left to right, all results mod 7): a + b = (a + b) mod 7 a - b = (a - b) mod 7 a * b = (a × b) mod 7 a / b = (a × b⁻¹) mod 7 [b≠0]. | F#N := K#O / I#K. I#K := 6. K#O := 6. G#M := 3. E#O := 2. | F#N | 1 | I#K = 6 -> I#K = 6
K#O = 6 -> K#O = 6
F#N = K#O / I#K
= 6 / 6
6 / 6 = (6 × 6⁻¹) mod 7 = 1
=> F#N = 1 | [
{
"glyph": "+",
"kind": "add",
"params": {},
"definition": "a + b = (a + b) mod 7"
},
{
"glyph": "-",
"kind": "sub",
"params": {},
"definition": "a - b = (a - b) mod 7"
},
{
"glyph": "*",
"kind": "mul",
"params": {},
"definition": "a * b = (a × b) mod 7"
},
... | 2 | 2 | 5 | 3 | 0 | {
"G#M": 1,
"I#K": 1,
"E#O": 1,
"K#O": 1,
"F#N": 2
} | mod7_arith_d2_0098 |
7 | arith | Operator definitions (evaluate strictly left to right, all results mod 7): a + b = (a + b) mod 7 a - b = (a - b) mod 7 a * b = (a × b) mod 7 a / b = (a × b⁻¹) mod 7 [b≠0].
I#O := 1. L#I := G#J / I#O. G#J := 4. L#I? | Operator definitions (evaluate strictly left to right, all results mod 7): a + b = (a + b) mod 7 a - b = (a - b) mod 7 a * b = (a × b) mod 7 a / b = (a × b⁻¹) mod 7 [b≠0]. | I#O := 1. L#I := G#J / I#O. G#J := 4. | L#I | 4 | G#J = 4 -> G#J = 4
I#O = 1 -> I#O = 1
L#I = G#J / I#O
= 4 / 1
4 / 1 = (4 × 1⁻¹) mod 7 = 4
=> L#I = 4 | [
{
"glyph": "+",
"kind": "add",
"params": {},
"definition": "a + b = (a + b) mod 7"
},
{
"glyph": "-",
"kind": "sub",
"params": {},
"definition": "a - b = (a - b) mod 7"
},
{
"glyph": "*",
"kind": "mul",
"params": {},
"definition": "a * b = (a × b) mod 7"
},
... | 2 | 2 | 3 | 3 | 0 | {
"G#J": 1,
"I#O": 1,
"L#I": 2
} | mod7_arith_d2_0099 |
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