Nuprl Lemma : geo-cong-preserves-lt
∀e:BasicGeometry. ∀p,q,p1,q1:Length. (p < q ⇒ (p = p1 ∈ Length) ⇒ (q = q1 ∈ Length) ⇒ p1 < q1)
Proof
Definitions occuring in Statement :
geo-lt: p < q,
geo-length-type: Length,
basic-geometry: BasicGeometry,
all: ∀x:A. B[x],
implies: P ⇒ Q,
equal: s = t ∈ T
Definitions unfolded in proof :
all: ∀x:A. B[x],
implies: P ⇒ Q,
prop: ℙ,
member: t ∈ T,
squash: ↓T,
uall: ∀[x:A]. B[x],
true: True
Lemmas referenced :
geo-lt_wf,
squash_wf,
true_wf,
geo-length-type_wf,
basic-geometry_wf
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
lambdaFormation_alt,
cut,
hypothesis,
hyp_replacement,
thin,
equalitySymmetry,
sqequalRule,
applyEquality,
lambdaEquality_alt,
sqequalHypSubstitution,
imageElimination,
introduction,
extract_by_obid,
isectElimination,
hypothesisEquality,
equalityTransitivity,
universeIsType,
inhabitedIsType,
natural_numberEquality,
imageMemberEquality,
baseClosed,
equalityIstype,
because_Cache
Latex:
\mforall{}e:BasicGeometry. \mforall{}p,q,p1,q1:Length. (p < q {}\mRightarrow{} (p = p1) {}\mRightarrow{} (q = q1) {}\mRightarrow{} p1 < q1)
Date html generated:
2019_10_16-PM-01_19_09
Last ObjectModification:
2019_03_04-PM-04_21_09
Theory : euclidean!plane!geometry
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