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Proof step 46 from proof ex-validrefs-fits-stronger (previous step)

# sks = # refs1, st[r -- i '] = refval(r0), fits(r0, sks, st), validrefs(str, r0 ' + refs1, st[r -- _type] .type .type, st), i < st[r -- _length] .intval, st[r -- _type] .type ≤ ty, is_array(str, r, st), 0 < st[r -- _length] .intval, 0 ≤ i, ∀ n. n ≠ 0 ∧ ¬ # refs1 < n → st[r0 -- firstn(n, sks)] .refval = (r0 ' + refs1)[n], ∀ st0, ty, r1, str, refs. # refs < # (r0 + refs1) → ( validrefs(str, r1 ' + refs, ty, st0) → (∃ sks. fits(r1, sks, st0) ∧ # sks = # refs ∧ (∀ n. n ≠ 0 ∧ n ≤ # sks → st0[r1 -- firstn(n, sks)] .refval = (r1 ' + refs)[n]))) ⊦ r = jvmref, fits(r, i ' + sks, st) ∧ # (i ' + sks) = 1 + # refs1 ∧ (∀ n. n ≠ 0 ∧ n ≤ # (i ' + sks) → st[r -- firstn(n, i ' + sks)] .refval = (r ' + r0 ' + refs1)[n])

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 45:
# sks = # refs1, st[r -- i '] = refval(r0), fits(r0, sks, st), validrefs(str, r0 ' + refs1, st[r -- _type] .type .type, st), i < st[r -- _length] .intval, st[r -- _type] .type ≤ ty, is_array(str, r, st), 0 < st[r -- _length] .intval, 0 ≤ i, ∀ n. n ≠ 0 ∧ ¬ # refs1 < n → st[r0 -- firstn(n, sks)] .refval = (r0 ' + refs1)[n], ∀ st0, ty, r1, str, refs. # refs < # (r0 + refs1) → ( validrefs(str, r1 ' + refs, ty, st0) → (∃ sks. fits(r1, sks, st0) ∧ # sks = # refs ∧ (∀ n. n ≠ 0 ∧ n ≤ # sks → st0[r1 -- firstn(n, sks)] .refval = (r1 ' + refs)[n]))) ⊦ r = jvmref, fits(r, i ' ' + sks, st) ∧ (n ≠ 0 ∧ n ≤ 1 + # refs1 → st[r -- firstn(n, i ' ' + sks)] .refval = (r ' + r0 ' + refs1)[n])

Rule argument

[emptyarg]

Additional information

[[CONCRETESIMPRULES : ([CSIMPSEQ : ⊦ m + n = n + m], [CSIMPSEQ : ⊦ (m + n0) + n1 = m + n0 + n1], [CSIMPSEQ : ⊦ m + n = m + n0 ↔ n = n0], [CSIMPSEQ : ⊦ (sks + sks0) + sks1 = sks + sks0 + sks1], [CSIMPSEQ : ⊦ # sk ' = 0 +1], [CSIMPSEQ : ⊦ # (sks + sks0) = # sks + # sks0], [CSIMPSEQ : ⊦ sk + sks = sk ' + sks])]]