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Proof step 87 from proof push-corr (previous step)

buf .size = n→i(# buf .data), (buf .first + buf .len) % buf .size < 0, buf .len < buf .size, buf .first < buf .size, buf .len ≤ buf .size, 0 ≤ buf .len, 0 < buf .size, 0 ≤ buf .first ⊦ buf .size = 0

User applied rule insert elim lemma

And closed the goal!

Rule argument

[x0lemmaarg: spec-name: int-div instance-name: lemma-name: div-elim antecedent: succedent: 0 < j ∧ 0 < i → ( i0 = i / j ∧ j0 = i % j ↔ i = i0 * j + j0 ∧ 0 ≤ j0 ∧ j0 < j) substlist: [i, j, i0, j0] → [buf .first + buf .len, buf .size, i, j] add preconditions?: F is rewrite lemma?: F current spec?: F rotate lemma?: F replace all?: F paths: () dummy: () ]

Additional information

[[CONCRETESIMPRULES : ([CSIMPSEQ : ⊦ i < j → (¬ ¬ j ≤ i ↔ false)], [CSIMPSEQ : ⊦ ¬ i < j ↔ j ≤ i], [CSIMPSEQ : ⊦ i + j + i0 = (i + j) + i0], [CSIMPSEQ : ⊦ i + j = j + i], [CSIMPFORWARD : ⊦ i ≤ j ∧ j < j0 → i < j0], [CSIMPFORWARD : ⊦ j ≤ j0 ∧ j0 ≤ j1 → j ≤ j1], [CSIMPFORWARD : ⊦ j ≤ i ∧ i ≤ 0 → j ≤ 0], [CSIMPSEQ : ⊦ i + j ≤ i ↔ j ≤ 0], [CSIMPSEQ : ⊦ i ≤ j → (j ≤ i ↔ i = j)], [CSIMPFORWARD : ⊦ i < j ∧ j ≤ j0 → i < j0], [CSIMPSEQ : j ≠ 0 ⊦ 0 % j = 0], [CSIMPELIM : ⊦ 0 < j ∧ 0 < i → ( i0 = i / j ∧ j0 = i % j ↔ i = i0 * j + j0 ∧ 0 ≤ j0 ∧ j0 < j)])], [EXTRATERMS : (buf .first + buf .len, buf .size, i, j)]]