Nuprl Lemma : ex-approx-context
∀[e:Atom2]. ∀[a,b,g:Base].  (ex-approx(e;g a;g b)) supposing (ex-approx(e;a;b) and e#g:Base)
Proof
Definitions occuring in Statement : 
ex-approx: ex-approx(e;t;t')
, 
free-from-atom: a#x:T
, 
atom: Atom$n
, 
uimplies: b supposing a
, 
uall: ∀[x:A]. B[x]
, 
apply: f a
, 
base: Base
Definitions unfolded in proof : 
prop: ℙ
, 
squash: ↓T
, 
implies: P 
⇒ Q
, 
sq_stable: SqStable(P)
, 
member: t ∈ T
, 
uimplies: b supposing a
, 
uall: ∀[x:A]. B[x]
, 
ex-approx: ex-approx(e;t;t')
, 
all: ∀x:A. B[x]
, 
compose: f o g
Lemmas referenced : 
base_wf, 
free-from-atom_wf2, 
ex-approx_wf, 
sq_stable__ex-approx, 
istype-universe
Rules used in proof : 
atomnEquality, 
because_Cache, 
imageElimination, 
imageMemberEquality, 
independent_functionElimination, 
hypothesis, 
baseClosed, 
closedConclusion, 
baseApply, 
sqequalRule, 
hypothesisEquality, 
thin, 
isectElimination, 
sqequalHypSubstitution, 
extract_by_obid, 
introduction, 
cut, 
isect_memberFormation, 
sqequalReflexivity, 
computationStep, 
sqequalTransitivity, 
sqequalSubstitution, 
lambdaFormation_alt, 
inhabitedIsType, 
dependent_functionElimination, 
freeFromAtomApplication, 
freeFromAtomTriviality, 
lambdaEquality_alt, 
functionExtensionality
Latex:
\mforall{}[e:Atom2].  \mforall{}[a,b,g:Base].    (ex-approx(e;g  a;g  b))  supposing  (ex-approx(e;a;b)  and  e\#g:Base)
Date html generated:
2020_05_20-AM-09_08_06
Last ObjectModification:
2020_01_10-PM-03_37_42
Theory : minimal-first-order-logic
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