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Theorem modmod-add-if3

0 < j ⊦ (i + i0 % j) % j = (0 ≤ i + i0 % j ∧ i + i0 < 0 ∧ 0 ≤ i ∧ i0 < 0 ∧ (i + i0 % j) % j ≠ 0 ⊃ (i + i0) % j + j ;(i + i0 % j < 0 ∧ 0 ≤ i + i0 ∧ i < 0 ∧ 0 ≤ i0 ∧ (i + i0 % j) % j ≠ 0 ⊃ (i + i0) % j - j;(i + i0) % j) )

Type: A user defined theorem
Validity: The proof is valid.
Features:
Comment:
Used by:
Used by units in proved state:
Proof exists?: Yes

View the proof

Infos about the proof

Proved?: Yes
Interactions: 1
Proof steps: 19
Used lemmas: modmod-add2-negpos-neg, modmod-add-zero, mod-less-01, modmod-add2-posneg-neg, mod-neq, mod-neq-01, modmod-add-if,
Used spec theorems:
- Used simplifier rules: