Nuprl Lemma : rcos_functionality
∀[x,y:ℝ]. rcos(x) = rcos(y) supposing x = y
Proof
Definitions occuring in Statement :
rcos: rcos(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,
implies: P ⇒ Q,
prop: ℙ,
uiff: uiff(P;Q),
and: P ∧ Q,
rev_uimplies: rev_uimplies(P;Q)
Lemmas referenced :
req_witness,
rcos_wf,
req_wf,
real_wf,
cosine_wf,
req_weakening,
req_functionality,
req_transitivity,
rcos-is-cosine,
cosine_functionality
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
isect_memberFormation,
introduction,
cut,
extract_by_obid,
sqequalHypSubstitution,
isectElimination,
thin,
hypothesisEquality,
hypothesis,
independent_functionElimination,
sqequalRule,
isect_memberEquality,
because_Cache,
equalityTransitivity,
equalitySymmetry,
independent_isectElimination,
productElimination
Latex:
\mforall{}[x,y:\mBbbR{}]. rcos(x) = rcos(y) supposing x = y
Date html generated:
2016_10_26-PM-00_14_38
Last ObjectModification:
2016_09_12-PM-05_40_26
Theory : reals_2
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