Nuprl Lemma : expr_functionality
∀[x,y:ℝ]. expr(x) = expr(y) supposing x = y
Proof
Definitions occuring in Statement :
expr: expr(x),
req: x = y,
real: ℝ,
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,
subtype_rel: A ⊆r B,
prop: ℙ,
uiff: uiff(P;Q),
and: P ∧ Q,
rev_uimplies: rev_uimplies(P;Q),
implies: P ⇒ Q
Lemmas referenced :
req_functionality,
expr_wf,
real_wf,
req_wf,
rexp_wf,
expr-req,
req_witness,
req_weakening,
rexp_functionality
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
isect_memberFormation,
introduction,
cut,
extract_by_obid,
sqequalHypSubstitution,
isectElimination,
thin,
hypothesisEquality,
hypothesis,
applyEquality,
lambdaEquality,
setElimination,
rename,
setEquality,
sqequalRule,
independent_isectElimination,
productElimination,
independent_functionElimination,
isect_memberEquality,
because_Cache,
equalityTransitivity,
equalitySymmetry
Latex:
\mforall{}[x,y:\mBbbR{}]. expr(x) = expr(y) supposing x = y
Date html generated:
2017_10_04-PM-10_38_03
Last ObjectModification:
2017_06_24-AM-11_02_53
Theory : reals_2
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