Nuprl Lemma : callbyvalueall-apply
∀[g:Base]. ∀[a,F:Top]. (let f ⟵ g in let x ⟵ f a in F[x] ~ let x ⟵ g a in F[x]) supposing g ~ λx.(g x)
Proof
Definitions occuring in Statement :
callbyvalueall: callbyvalueall,
uimplies: b supposing a,
uall: ∀[x:A]. B[x],
top: Top,
so_apply: x[s],
apply: f a,
lambda: λx.A[x],
base: Base,
sqequal: s ~ t
Definitions unfolded in proof :
uall: ∀[x:A]. B[x],
member: t ∈ T,
uimplies: b supposing a,
callbyvalueall: callbyvalueall,
evalall: evalall(t)
Lemmas referenced :
top_wf,
base_sq,
base_wf
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
isect_memberFormation,
introduction,
cut,
sqequalRule,
hypothesis,
callbyvalueReduce,
sqleReflexivity,
sqequalAxiom,
lemma_by_obid,
sqequalHypSubstitution,
isect_memberEquality,
isectElimination,
thin,
hypothesisEquality,
because_Cache,
sqequalIntensionalEquality,
equalityTransitivity,
equalitySymmetry
Latex:
\mforall{}[g:Base]
\mforall{}[a,F:Top]. (let f \mleftarrow{}{} g in let x \mleftarrow{}{} f a in F[x] \msim{} let x \mleftarrow{}{} g a in F[x]) supposing g \msim{} \mlambda{}x.(g x)
Date html generated:
2016_05_15-PM-02_08_47
Last ObjectModification:
2015_12_27-AM-00_36_31
Theory : untyped!computation
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