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Proof step 5 from proof decode-contract (previous step)

EB_PAGE_SIZE ≤ # buf, ENCODED_ELEM_SIZE ≤ EB_PAGE_SIZE, ENCODED_ELEM_SIZE ≤ # buf ⊦ ⟪decode_nonempty#(0, buf; a; err)⟫ ((err = ESUCCESS ∨ ⌊err⌋ ) ∧ (err = ESUCCESS → is-encoded-pagesize(a, subarray(buf, 0, EB_PAGE_SIZE))))

User applied rule insert program lemma

And obtained the following new goals

Proof step 6:
n + ENCODED_ELEM_SIZE ≤ # buf ⊦ ⟪decode_nonempty#(n, buf; a; err)⟫ ((err = ESUCCESS ∨ ⌊err⌋ ) ∧ (err = ESUCCESS → is-encoded-nonempty(a, subarray(buf, n, ENCODED_ELEM_SIZE))))
Proof step 7:
buf0 = buf, n0 = 0, ENCODED_ELEM_SIZE ≤ # buf, ENCODED_ELEM_SIZE ≤ EB_PAGE_SIZE, EB_PAGE_SIZE ≤ # buf, 0 + ENCODED_ELEM_SIZE ≤ # buf ⊦ [decode_nonempty#(0, buf; a; err)] ( (err = ESUCCESS ∨ ⌊err⌋ ) ∧ (err = ESUCCESS → is-encoded-nonempty(a, subarray(buf0, n0, ENCODED_ELEM_SIZE))) → (err = ESUCCESS ∨ ⌊err⌋ ) ∧ (err = ESUCCESS → is-encoded-pagesize(a, subarray(buf, 0, EB_PAGE_SIZE))))

Rule argument

spec: encoding-fixed-size-nonempty name: decode-contract seq: n + ENCODED_ELEM_SIZE ≤ # buf ⊦ ⟪decode_nonempty#(n, buf; a; err)⟫ ( (err = ESUCCESS ∨ ⌊err⌋ ) ∧ ( err = ESUCCESS → is-encoded-nonempty (a, subarray(buf, n, ENCODED_ELEM_SIZE)))) subst: [buf, n, a, err] → [buf, 0, a, err] flags: <all paths>

Additional information

Used simplifier rules: ⊦ n + 0 = n; (s)%a: ⊦ (m + n0) + n1 = m + n0 + n1; from specification nat-basic%c: ⊦ m + n = n + m; from specification nat-basic% ⊦ m ≤ n ↔ ¬ n < m; (ss)% ⊦ m ≤ n → (n < m ↔ false); (s)