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Proof step 38 from proof ex-validrefs-fits-stronger (previous step)

firstn(m, sks) ≠ [], st[r -- i '] = refval(r0), # sks = # refs1, 0 ≤ i, 0 < st[r -- _length] .intval, is_array(str, r, st), st[r -- _type] .type ≤ ty, i < st[r -- _length] .intval, validrefs(str, r0 ' + refs1, st[r -- _type] .type .type, st), fits(r0, sks, st), m ≤ # refs1, ∀ 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, st[st[r -- i '] .refval -- firstn(m, sks)] .refval = (r0 ' + refs1)[m], is_classtype(st[r -- _type] .type)

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 37:
# sks = # refs1, st[r -- i '] = refval(r0), m ≤ # refs1, 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, m = 0, st[r0 -- firstn(m, sks)] .refval = (r0 ' + refs1)[m], is_classtype(st[r -- _type] .type)

Rule argument

[emptyarg]

Additional information

[[CONCRETESIMPRULES : ([CSIMPSEQ : ⊦ refval(r) .refval = r], [CSIMPSEQ : ⊦ firstn(n, sks) = [] ↔ n = 0])]]