Nuprl Lemma : req_int_terms_transitivity
∀[t1,t2,t3:int_term()]. (t1 ≡ t3) supposing (t2 ≡ t3 and t1 ≡ t2)
Proof
Definitions occuring in Statement :
req_int_terms: t1 ≡ t2,
int_term: int_term(),
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,
req_int_terms: t1 ≡ t2,
all: ∀x:A. B[x],
implies: P ⇒ Q,
prop: ℙ,
guard: {T},
uiff: uiff(P;Q),
and: P ∧ Q,
rev_uimplies: rev_uimplies(P;Q)
Lemmas referenced :
real_wf,
req_witness,
real_term_value_wf,
req_int_terms_wf,
int_term_wf,
req_functionality,
req_weakening
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
isect_memberFormation,
introduction,
cut,
sqequalHypSubstitution,
lambdaFormation,
functionEquality,
intEquality,
extract_by_obid,
hypothesis,
sqequalRule,
lambdaEquality,
dependent_functionElimination,
thin,
hypothesisEquality,
isectElimination,
functionExtensionality,
applyEquality,
independent_functionElimination,
isect_memberEquality,
because_Cache,
equalityTransitivity,
equalitySymmetry,
independent_isectElimination,
productElimination
Latex:
\mforall{}[t1,t2,t3:int\_term()]. (t1 \mequiv{} t3) supposing (t2 \mequiv{} t3 and t1 \mequiv{} t2)
Date html generated:
2017_10_02-PM-07_18_34
Last ObjectModification:
2017_04_02-PM-11_44_48
Theory : reals
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