Nuprl Lemma : equiv_int_terms_weakening
∀[t1,t2:int_term()]. t1 ≡ t2 supposing t1 = t2 ∈ int_term()
Proof
Definitions occuring in Statement :
equiv_int_terms: t1 ≡ t2,
int_term: int_term(),
uimplies: b supposing a,
uall: ∀[x:A]. B[x],
equal: s = t ∈ T
Definitions unfolded in proof :
uall: ∀[x:A]. B[x],
member: t ∈ T,
uimplies: b supposing a,
equiv_int_terms: t1 ≡ t2,
all: ∀x:A. B[x],
and: P ∧ Q,
prop: ℙ
Lemmas referenced :
and_wf,
equal_wf,
int_term_wf,
int_term_value_wf
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
isect_memberFormation,
introduction,
cut,
lambdaFormation,
equalitySymmetry,
dependent_set_memberEquality,
hypothesis,
independent_pairFormation,
hypothesisEquality,
lemma_by_obid,
sqequalHypSubstitution,
isectElimination,
thin,
applyEquality,
lambdaEquality,
setElimination,
rename,
productElimination,
setEquality,
functionEquality,
intEquality,
sqequalRule,
dependent_functionElimination,
axiomEquality,
isect_memberEquality,
because_Cache,
equalityTransitivity
Latex:
\mforall{}[t1,t2:int\_term()]. t1 \mequiv{} t2 supposing t1 = t2
Date html generated:
2016_05_14-AM-06_59_46
Last ObjectModification:
2015_12_26-PM-01_12_40
Theory : omega
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