Nuprl Lemma : equiv_int_terms_functionality
∀[x1,x2,y1,y2:int_term()]. (uiff(x1 ≡ y1;x2 ≡ y2)) supposing (y1 ≡ y2 and x1 ≡ x2)
Proof
Definitions occuring in Statement :
equiv_int_terms: t1 ≡ t2,
int_term: int_term(),
uiff: uiff(P;Q),
uimplies: b supposing a,
uall: ∀[x:A]. B[x]
Definitions unfolded in proof :
uall: ∀[x:A]. B[x],
member: t ∈ T,
uimplies: b supposing a,
uiff: uiff(P;Q),
and: P ∧ Q,
equiv_int_terms: t1 ≡ t2,
all: ∀x:A. B[x],
prop: ℙ,
squash: ↓T,
true: True,
subtype_rel: A ⊆r B,
guard: {T},
iff: P ⇐⇒ Q,
rev_implies: P ⇐ Q,
implies: P ⇒ Q
Lemmas referenced :
equiv_int_terms_wf,
int_term_wf,
equal_wf,
squash_wf,
true_wf,
int_term_value_wf,
iff_weakening_equal
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
isect_memberFormation,
introduction,
cut,
independent_pairFormation,
sqequalHypSubstitution,
lambdaFormation,
hypothesis,
functionEquality,
intEquality,
sqequalRule,
lambdaEquality,
dependent_functionElimination,
thin,
hypothesisEquality,
axiomEquality,
extract_by_obid,
isectElimination,
productElimination,
independent_pairEquality,
isect_memberEquality,
because_Cache,
equalityTransitivity,
equalitySymmetry,
applyEquality,
imageElimination,
universeEquality,
functionExtensionality,
natural_numberEquality,
imageMemberEquality,
baseClosed,
independent_isectElimination,
independent_functionElimination
Latex:
\mforall{}[x1,x2,y1,y2:int\_term()]. (uiff(x1 \mequiv{} y1;x2 \mequiv{} y2)) supposing (y1 \mequiv{} y2 and x1 \mequiv{} x2)
Date html generated:
2017_04_14-AM-08_57_35
Last ObjectModification:
2017_02_27-PM-03_40_56
Theory : omega
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