Nuprl Lemma : insert-combine-nil
∀cmp,f,x:Top. (insert-combine(cmp;f;x;[]) ~ [x])
Proof
Definitions occuring in Statement :
insert-combine: insert-combine(cmp;f;x;l),
cons: [a / b],
nil: [],
top: Top,
all: ∀x:A. B[x],
sqequal: s ~ t
Definitions unfolded in proof :
insert-combine: insert-combine(cmp;f;x;l),
all: ∀x:A. B[x],
so_lambda: so_lambda(x,y,z.t[x; y; z]),
member: t ∈ T,
top: Top,
so_apply: x[s1;s2;s3]
Lemmas referenced :
list_ind_nil_lemma,
top_wf
Rules used in proof :
sqequalSubstitution,
sqequalRule,
sqequalReflexivity,
sqequalTransitivity,
computationStep,
cut,
lemma_by_obid,
sqequalHypSubstitution,
dependent_functionElimination,
thin,
isect_memberEquality,
voidElimination,
voidEquality,
hypothesis,
lambdaFormation
Latex:
\mforall{}cmp,f,x:Top. (insert-combine(cmp;f;x;[]) \msim{} [x])
Date html generated:
2016_05_14-PM-02_41_01
Last ObjectModification:
2015_12_26-PM-02_43_45
Theory : list_1
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