Nuprl Lemma : has-valueall-apply
∀[a,g:Base]. has-valueall(g) supposing has-valueall(g a)
Proof
Definitions occuring in Statement :
has-valueall: has-valueall(a),
uimplies: b supposing a,
uall: ∀[x:A]. B[x],
apply: f a,
base: Base
Definitions unfolded in proof :
prop: ℙ,
has-value: (a)↓,
has-valueall: has-valueall(a),
uimplies: b supposing a,
member: t ∈ T,
uall: ∀[x:A]. B[x],
evalall: evalall(t),
all: ∀x:A. B[x],
implies: P ⇒ Q,
or: P ∨ Q,
top: Top,
not: ¬A,
false: False,
outl: outl(x),
outr: outr(x)
Lemmas referenced :
bottom_diverge,
has-value-implies-dec-ispair,
bottom-sqle,
has-value-implies-dec-isinl,
has-value-implies-dec-isinr,
has-valueall-has-value,
has-valueall_wf_base,
base_wf
Rules used in proof :
equalitySymmetry,
equalityTransitivity,
because_Cache,
isect_memberEquality,
axiomSqleEquality,
callbyvalueApply,
hypothesis,
independent_isectElimination,
hypothesisEquality,
baseClosed,
closedConclusion,
baseApply,
sqequalRule,
thin,
isectElimination,
sqequalHypSubstitution,
lemma_by_obid,
cut,
introduction,
isect_memberFormation,
sqequalReflexivity,
computationStep,
sqequalTransitivity,
sqequalSubstitution,
extract_by_obid,
callbyvalueReduce,
dependent_functionElimination,
independent_functionElimination,
unionElimination,
sqequalSqle,
applyPair,
voidElimination,
voidEquality,
applyInl,
applyInr
Latex:
\mforall{}[a,g:Base]. has-valueall(g) supposing has-valueall(g a)
Date html generated:
2019_06_20-PM-00_26_52
Last ObjectModification:
2018_08_16-AM-11_10_30
Theory : fun_1
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